







Une autre bille de rayon différent 
20020227 

Sarah pose la question : une bille de 6 cm repose au fond d'1 cylindre droit dont la base est un disque de rayon 10 cm. On verse de l'eau dans le cylindre de façon à recouvrir exactement la bille. Démontrez que l'on peut remplacer la bille par une autre bille de rayon différent (mais supérieur) de sorte que l'eau initialement versée recouvre exactement cette nouvelle bille Claude Tardif lui répond. 





The derivative of f(x)=2^x/x 
20171128 

Chhavi pose la question : f(x)=2^x/x.
Find f'(x). Penny Nom lui répond. 





Average price 
20170915 

Annette pose la question : If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price Penny Nom lui répond. 





Differentiate y = x^x^x 
20170319 

Nafis pose la question : differentiate y = x^x^x Penny Nom lui répond. 





The derivative of the inverse of a function 
20161028 

Kate pose la question : Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^1(4) if f(3)=4 and f'(3)=1/7 Penny Nom lui répond. 





Subtraction of two numbers in different bases 
20161007 

Wica pose la question : Hello,
So happy I found this site. I am having problems with bases. My question is :
Please perform the subtraction between two number over different bases :
A. (5874)base 12  (216)base 9
B. (216)base 9  (5874)base 12 Penny Nom lui répond. 





Implicit differentiation 
20160606 

Pranay pose la question : Is a circle x^2+y^2=2 a function? If it is not a function,
why is it possible to do implicit differentiation on it?
Thanks. Penny Nom lui répond. 





A tangent line to a parabola 
20151202 

pei pose la question : Given that the line y=mx5 is a tangent to the curve y=2x^2+3 find the positive value of M. Penny Nom lui répond. 





The derivative of x^1/3 
20151108 

omar pose la question : hi can help me
am teacher ask me about x^1/3 Derivation definition . Penny Nom lui répond. 





Two cars approaching an intersection 
20150416 

Engabu pose la question : Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection? Penny Nom lui répond. 





Integers in different bases 
20150305 

Michael pose la question : Let k be a positive integer so that 28 (subscript)k = 132 (subscript)5 Penny Nom lui répond. 





f(x)=(x^21)/(x1) 
20150221 

Ahmed pose la question : Is f(x)=[(x^21)/(x1) and x=2 at x=1] differentiable at x=1 ? Why ? Penny Nom lui répond. 





Differentiate ln[x(2x4)^1/2] 
20140628 

Igwe pose la question : If y=In[x(2x4)^1/2],find dy/dx at x=3 Penny Nom lui répond. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

sudhir pose la question : the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Penny Nom lui répond. 





A number with all the digits different 
20140207 

Jon pose la question : I'm not a mathematician but just curious. Is there a name for a number of up to ten digits where each digit is different,
i.e the equivalent of an isogram in linguistics? My online banking gives me a random 8digit number each time I log on
and it is rare to get one of the type I refer to. There must be calculable odds, but I'm only allowed one question!
Thanks in advance
Jon Harley Weston lui répond. 





Differentiate x^x  2^sinx 
20130809 

tarun pose la question : derivative of x^x  2^sinx Penny Nom lui répond. 





f(x) + f ''''(x)=0 
20130305 

Andreea pose la question : Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something. Brennan Yaremko lui répond. 





The multiplication table for the different bases 
20130201 

sylvia pose la question : I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers. Penny Nom lui répond. 





The derivative of y = sin (30º + x) 
20121107 

Saskia pose la question : derivative of y = sin (30º + x) Harley Weston lui répond. 





An implicit differentiation problem 
20121026 

Katie pose la question : find y' of x^2y2y^3=3x+2y Harley Weston lui répond. 





Differentiation rules 
20121023 

Morgan pose la question : Use the derivative rules to differentiate each of the following:
1. f(x)=1/x1 2. f(x)= sqrt(x) Penny Nom lui répond. 





The derivative of 2sin cubed x  3 sin x 
20120325 

holly pose la question : suppose f(x) = 2sin cubed x  3 sin x
show that f 1(x) = 3 cos x cos 2x Harley Weston lui répond. 





Integral 1/(25x^2)^3/2 
20120222 

John pose la question : Integral 1/(25x^2)^3/2 Harley Weston lui répond. 





Dt[sin t tan (t^2+1)] 
20120221 

Ayu pose la question : Ayu
Dt[sin t tan (t^2+1)]
derivatives Harley Weston lui répond. 





Notation for the second derivative 
20120206 

Shafira pose la question : In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2? Robert Dawson lui répond. 





The derivative of x^(1/2) 
20120114 

Eric pose la question : I have an problem figuring out the derivative of the negative square root of x i.e. x^(1/2) using the first principle.
Could someone please show me?
Thanks in advance! Harley Weston lui répond. 





The number of digits in a number base m 
20111222 

Jash pose la question : Assume there is a number system of base m.
The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b).
In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant.
Find m. Robert Dawson lui répond. 





Implicit differentiation 
20111020 

Monica pose la question : Find dy/dx in terms of x and y, if sin(xy)=(x^2)y. Penny Nom lui répond. 





The derivative of f(x) = (x+1)^1/2 
20110905 

Carla pose la question : Find the derivative using the limit process of
f(x) = (x+1)^1/2 Harley Weston lui répond. 





Differentiable on an interval 
20100812 

Dave pose la question : Hi
I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help. Robert Dawson lui répond. 





The rate of change of y with respect to x 
20100429 

Tom pose la question : I just had a quick calc question about wording that wasn't ever
addressed in class. When the book says "the rate of change of y with
respect to x", should it be considered how fast y is changing in
comparison to x?
I ask because the textbook says that "y is changing 3 times faster than x,
so the rate of change of y with respect to x is 3." I'm use to rate being
like velocity, as in units of distance per units of time. All we're told
in class is that it's the slope of the tangent line, I was hoping you
could clarify for me what exactly is meant by the wording of a "rate of
change of something with respect to something else". More specifically, what
"rate" and "with respect to" mean within this context?
Thanks for your time Harley Weston lui répond. 





The derivative of cos^3x 
20100406 

Erson pose la question : Find y' of the given function: y = cos^3x. Harley Weston lui répond. 





The nth derivative of x^(n1) log x 
20100310 

shambodeb pose la question : This is a successive differentiation problem by Leibnitz theorem
If y = x^{n1} log x ; Proof nth derivative y^{(n)} = (n1)!/x Harley Weston lui répond. 





Painting a dome 
20091030 

Jessica pose la question : A hemispherical dome with a radius of 50 ft will be given a coat of paint .01 inch thick.
The Contractor for the job wants to estimate the number of gallons of paint needed.
Use a differential to obtain an estimate (231 cubic inches/gallon) HINT: Approximate the change
in volume of hemisphere corresponding to increase of .01 inch in the radius. Robert Dawson lui répond. 





Differentiating y= square root(x1) 
20090929 

edith pose la question : describe the xvalues at which f is differentiable.
y= square root(x1) Penny Nom lui répond. 





Maximum Volume of a Cylinder Inscribed in a Sphere 
20090618 

Jim pose la question : Hello I have a hard time finishing this question:
A right circular cylinder has to be designed to sit inside a sphere of radius 6 meters
so that each top and bottom of the cylinder touches the sphere along its complete
circular edge. What are the dimensions of the cylinder of max volume and what is the volume? Janice Cotcher lui répond. 





differentiate y sin[x^2]=x sin[y^2] 
20090511 

mamiriri pose la question : derivate y sin[x^2]=x sin[y^2] Harley Weston lui répond. 





Implicit differentiation 
20090301 

Emily pose la question : determine the derivative y' at the point (1,0)
y= ln(x^2+y^2)
y'(1)= ?? Stephen La Rocque lui répond. 





Multiplying in different bases 
20090225 

Susan pose la question : 11 base 2 X 22 base 3 + 33 base 4 = _________ base 5 Robert Dawson lui répond. 





Implicit differentiation 
20090218 

Sunny pose la question : Find slope of the tangent line to the curve 2(x^2+y^2)2=25(x^2–y^2) at (3,1) Robert Dawson and Harley Weston lui répond. 





In what base is 3x3= 10? 
20090214 

David pose la question : In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one? Penny Nom lui répond. 





What's the derivative of y = e^2xe^2x / e^2x+e^2x? 
20090202 

Heather pose la question : What's the derivative of y = e^2xe^2x / e^2x+e^2x ? Harley Weston lui répond. 





Determine y'' by implicitly differentiating twice 
20090104 

Walter pose la question : Given x^3  3xy + y^3 = 1 , determine y'' by implicitly differentiating
twice. I cannot solve this. Would you be kind enough to perform the
mathematics and show the steps involved in obtaining the solution? Harley Weston lui répond. 





Division in different bases 
20081202 

MICHELLE pose la question : DIVIDE 538 BY 14 IN BASE 2, 3, 4 & 5 Penny lui répond. 





Separating variables 
20081104 

Terry pose la question : by separating variables solve the initial value problem
(x+1)y' + y = 0 y(0) = 1 Harley Weston lui répond. 





Antiderivative of 1/(x(1  x)) 
20081022 

Matt pose la question : derivative of dx/(x(1x))
From what I've seen I should break apart the equation as such
derivative of dx/x  dx/(1x)
and then get the 2 corresponding log functions.
If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative. Harley Weston lui répond. 





Concavity and the second derivative 
20081015 

Christina pose la question : I'm having trouble solving for a second derivative for the following graphing question.
f(x) = (X^2+2x+4)/2x
using the quotient rule, I found:
f'(x) = (x^24)/(2x^2)
however, using the quotient rule again I can't seem to solve it (concavity):
f'''(x)=[(2x)(2x^2)(x^24)(4x)]/[(2x^2)^2]
f''(x)=[(4x^3(4x^3 16x)]/4x^4
f''(x)=16x/4x^4
f''(x)=4/x^3
and making the equation equal to zero result in 0=4 which doesn't seem to make sense... Penny Nom lui répond. 





A different approach to a word problem 
20081003 

Kenneth pose la question : Sarah's age is 2/3 of Mary's age and 3/4 of Ruth's age. The sum of their ages is 46 years. How old is each? Penny Nom lui répond. 





What is the derivative of (2^sinx)/(logbase4(2x+1))? 
20080916 

Jesse pose la question : What is the derivative of (2^sinx)/(logbase4(2x+1)) Harley Weston lui répond. 





Trough Filling with Water 
20080821 

lanny pose la question : a triangular trough is 10 feet long, 6 feet across the top, and 3 feet deep. if water flows at the rate of 12 cubic inches per minute, find how fast the surface is rising when the water is 6 inches deep. Janice Cotcher lui répond. 





A series solution of y' = xy 
20080703 

sasha pose la question : I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks Harley Weston lui répond. 





Differentiate y= (x^x^x)^x 
20080627 

emril pose la question : Differentiate y= (x^x^x)^x Harley Weston lui répond. 





f(x)=sin^3(3x^2) find f ' (x) 
20080421 

Michael pose la question : f(x)=sin^3(3x^2) find f ' (x) Harley Weston lui répond. 





The chain rule 
20080410 

joey pose la question : pls help me to Differentiate
y=(3x^24x)^8 Harley Weston lui répond. 





Differentiate 
20071228 

taiwo pose la question : i am finding it difficult to use first principle to differentiate this question: y=xcos2x. can u help me. Penny Nom lui répond. 





The tangent to a curve 
20071210 

Christy pose la question : I know this question is simple but I can't figure out what I'm doing wrong.
Find the equation of the tangent line to the curve 2x^2  y^4= 1 at the point (1,1). Penny Nom lui répond. 





The derivative 
20071119 

ralf pose la question : Find the derivative of the function
1. y=1+2x^{8}
2. y=(1+2x )^{8} Harley Weston lui répond. 





f(x+y) = f(x) + f(y) + 2xy 
20071101 

Marcia pose la question : For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h > 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x). Penny Nom lui répond. 





The rate of change of the concentration of a solution 
20071030 

Nicholas pose la question : A barrel initially has two kg of salt dissolved in twenty liters of water. If water flows in the rate of 0.4 liters per minute and the wellmixed salt water solution flow out at the same rate, how much salt is present after 8 minutes?
I tried working backwards given the answer but I can't seen to get their answer of ~1.7kg. Any help would be great! Thanks Harley Weston lui répond. 





The derivative of f(x)=1/(x1) 
20070921 

Michelle pose la question : im having trouble finding the derivative of f(x)=1/(x1) using the f(x+h)f(x)/h method. Stephen La Rocque lui répond. 





Differentiate x^(1/3) using first principles 
20070914 

Sheila pose la question : our teacher gave us this question as a challenge and even he couldnt figure it out:
Differentiate x^(1/3) [aka the cube root of x] using first principles. i know the answer is 1/(3.x^2/3), but how is it possible using first principles? Harley Weston lui répond. 





Solve y'' + y = 0 
20070728 

Shihya pose la question : How do you solve y’’ + y = 0 Stephen La Rocque and Harley Weston lui répond. 





Implicit Derivatives 
20070713 

Charles pose la question : I need help computing y' by implicit differentiation the question is:
y^2 + x/y + 4x^2  3 Stephen La Rocque lui répond. 





sinx and cosx 
20070625 

Mac pose la question : Can anyone tell me whether sinx and cosx is differentiable at x=0 ?
As far as i know, cos(x) and sin(x) is differentiable at all x. Penny Nom and Stephen La Rocque lui répond. 





The second derivative 
20070414 

Gerry pose la question : In mathematical context,what do you understand by the term "Second Derivative" Penny Nom lui répond. 





What is the intensity 5m below the surface? 
20070331 

david pose la question : I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help. Penny Nom lui répond. 





The period of a simple pendulum 
20070310 

Melissa pose la question : The period of a simple pendulum of length L feet is given by: T=2pi(sqrt(L/g))seconds. It is assumed that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.) Answer is in seconds. Melissa Penny Nom lui répond. 





Derivatives 
20070201 

Jacob pose la question : Find the derivative of: y= pi^2+x^2+3xy+sin(y^2) Penny Nom lui répond. 





Water is being pumped into the pool 
20061024 

Jon pose la question : A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end.
a) what percent of the pool is filled?
b) at what rate is the water level rising? Stephen La Rocque lui répond. 





Differentiate Y= sin3x + cos7x 
20060822 

james pose la question : Differentiate the function of x using the basic rules.
Y= sin3x + cos7x Stephen La Rocque lui répond. 





differentiate the volume of a cylinder with V respect to h 
20060524 

A student pose la question : differentiate the volume of a cylinder with V respect to h Stephen La Rocque lui répond. 





Rate of ladder falling 
20060430 

Harsh pose la question : A ladder 4 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 30 cm/s, how quickly is the top of the ladder sliding down the wall when the bottom of the ladder is 2 m from the wall? Stephen La Rocque lui répond. 





Differentiation, powers and logs 
20060106 

Claudia pose la question :
Question: how do I find the derivative of
x* ln(x+(e^2))^2
x^lnx
x^(e^(x^2))
Penny Nom lui répond. 





Notation for the second derivative 
20051108 

Mussawar pose la question : my question is ^{d}/_{dx}( ^{dy}/_{dx}) = ^{d2y}/_{dx2}. why it is not equal to ^{d2y}/_{d2x}. Penny Nom lui répond. 





Velocity and acceleration 
20051027 

Candace pose la question : When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared where do the units go when you make it an equation? How can a function be an area? Harley Weston lui répond. 





Can we take the derivative of independent variable 
20051018 

Mussawar pose la question : why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why. Walter Whiteley lui répond. 





U'(X)  U(X) = 0; U(0) = 2 
20050923 

David pose la question : Out of interest could you please answer the following questions?
U'(X)  U(X) = 0; U(0) = 2
and
U''(X)  U'(X) = 0; U'(0) = U(0) = 2
Harley Weston lui répond. 





How do you differentiate y=(x)^(x^x)? 
20050914 

Calebius pose la question : How do you differentiate y=(x)^{(xx)}? Penny Nom lui répond. 





Logarithmic differentiation 
20050523 

Richard pose la question : I need to convince myself that I understand the process of
differentiating y=x^{x}.
The specific question is that if I have to take the logarithm of both sides
of the equation how can differentiate the following?
y= {(x+2)^{(x+2)}}/{(x+1)^{(x+1)}}  {(x+1)^{(x+1)}}/(x^{x}),
I have an idea that the differential of this fairly complex function
is itself ... am I right or wrong. Penny Nom lui répond. 





Differentiating F(x,y) = 0 
20050123 

Jacob pose la question : In calculus, we often mention to the students that if F(x,y) = 0, then we can differentiate both sides and still get an equality. The problem is that we can't perform the same operation on F(x) = 0, say x = 0, otherwise 1 = 0, which is absurd. What is the reason? Walyer Whileley and Harley Weston lui répond. 





ln(x)/x 
20041211 

Tina pose la question : What is the derivative of (ln x)/x? The double derivative? Penny Nom lui répond. 





An ODE 
20041110 

David pose la question : I have a question that i really cant do, it is as follows:
The ODE dy/dx + 0.5y = 0.5e^(1.5x) ; y(5) = 2
Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 Harley Weston lui répond. 





Implicit differentiation 
20041024 

Emily pose la question : If x^3+3xy+2y^3=17, then in terms of x and y, dy/dx = Penny Nom lui répond. 





differentiate Y=X^X^X 
20040913 

Kunle pose la question : differentiate Y=X^X^X Penny Nom lui répond. 





The integrating factor method 
20040805 

A student pose la question : Whilst using the integrating factor method, I am required to integrate a function multipled by another function.
say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.
Integral f(t)*g(t) dt or
Integral exp(kt)*g(t) dt
What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k?
More specifically, the problem and my attempted answer is in PDF format:
In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Harley Weston lui répond. 





Differentiation 
20040804 

A parent pose la question : I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus:
a) f(x)=e^2^xIn(cos(8x))
b) f(x)=secx/SQRTx^4+1 Penny Nom lui répond. 





Some calculus problems 
20040401 

Weisu pose la question :
I have questions about three word problems and one
regular problem, all dealing with derivatives.
 Find all points on xy=e^{xy} where the tangent line
is horizontal.
 The width x of a rectangle is decreasing at 3 cm/s,
and its length y is increasing at 5 cm/s. At what rate
is its area A changing when x=10 and y=15?
 A car and a truck leave the same intersection, the
truck heading north at 60 mph and the car heading west
at 55 mph. At what rate is the distance between the
car and the truck changing when the car and the truck
are 30 miles and 40 miles from the intersection,
respectively?
 The production P of a company satisfies the
equation P=x^{2} + 0.1xy + y^{2}, where x and y are
the inputs. At a certain period x=10 units and y=8
units. Estimate the change in y that should be made to
set up a decrease of 0.5 in the input x so that the
production remains the same.
If you could just give me some hints on these
questions, I'd really appreciate it. Thanks! Penny Nom lui répond. 





A derivative 
20040331 

A student pose la question : What is the nth derivative of f(x) =(2x)/(1(x^{2}))? Harley Weston lui répond. 





A partial derivative 
20040319 

Penny Nom pose la question : Is it possible to differentiate the following equation, if so could
you please explain.
S=SQRT(T(5/X^2))
I would like the derivative of S with respect to X. Harley Weston lui répond. 





The derivative of x to the x 
20040214 

Cher pose la question : what about the derivative of x to the power x? Penny Nom lui répond. 





The slope of a tangent 
20031001 

A student pose la question :
find the slope of the tangent to each curve at the given point f(x)=square root 16x, where y=5 Penny Nom lui répond. 





Differentiating inverses 
20021120 

Amy pose la question : f(x)= x^{3}+x+1, a=1 find g'(a) (g = f^{ 1}). I am having trouble finding g(a). Penny Nom lui répond. 





Undetermined coefficients 
20011122 

Hoda pose la question : The equation is: y"  2y' + y = t e^{t} + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Ate^{t}+Be^{t}+C, but all I get is C=4 and I tried (At^{2}+Bt+C)e^{t}+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Harley Weston lui répond. 





A tangent line 
20011121 

A student pose la question : write an equation of the line tangent to the graph of
e^{y} + ln(xy) = 1 + e at (e,1) Harley Weston lui répond. 





4 sinx cosy = 1 
20011010 

A student pose la question : How would i differentiate the following example in terms of t (x and y are functions of t) 4 sinx cosy = 1 Claude Tardif lui répond. 





(x^25x6)/(x6) 
20011002 

Bill pose la question : given f(x) = (x^{2}5x6)/(x6) find f'(6). Harley Weston lui répond. 





National consumption function 
20010509 

Brian pose la question : If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Harley Weston lui répond. 





Differentiation 
20010417 

Esther pose la question : Could you please tell me what the first derivative is of the following: y = 2/(2x+e^{2x}) Is it (1+xe^{2x})/(2x+e^{2x})^{2} or perhaps 4(1+e^{2x})/(2x+e^{2x})^{2} ? I am a little confused between the two! Harley Weston lui répond. 





Airflow in windpipes 
20010325 

Ena pose la question : The volume of air flowing in windpipes is given by V=kpR^{4}, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro  R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that: 0 < 0.5*Ro < R < Ro, find the factor by which the radius of the windpipe contracts to give maximum flow? Harley Weston lui répond. 





A jogger 
20010312 

Bill pose la question : At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes. a) write an expression for the velocity of the jogger at time t. b) what is the total distance traveled by the jogger in that 10minute interval. Harley Weston lui répond. 





The domain of the derivative 
20010222 

Wayne pose la question : I know that the domain of f'(x) is a subset of the domain of f(x). Is it necessarily true that the subset will have at most one less element than the domain of the original function? Harley Wesston lui répond. 





Differentiation of y = x^{ n} 
20010217 

Jashan pose la question : i am studying differentation at the moment i have drawn some graphs such as y=x^{ 2}. i have found the formula for the gradient of this curve, this being 2x obtained by using differentation, but i need to know the general case for the formula where y=x^{n } in order for me to understand this topic more throughly, i would also like to know how u derived this general formula Harley Weston lui répond. 





Find an exprression for f(x) 
20010207 

A 12th grade AP Calc student pose la question : Let f be the function defined for all x > 5 and having the following properties. Find an expression for f(x). i) f^{ ''}(x) = 1/ (x+5)^{1/3} for all x in the domain of f ii) the line tangent to the graph of f at (4,2) has an angle of inclination of 45 degress. Harley Weston lui répond. 





How do you integrate secant(theta)? 
20001222 

Robert Williamson pose la question : How do you integrate secant(theta)? I know the answer is ln [sec(theta) + tan(theta)] but how do you get there? Claude tardif lui répond. 





Derivatives, there must be an easier way 
20000906 

Brad Goorman pose la question : The direction read: Take the derivative of each expression. y = {1+[x+(x^{2} +x^{3})^{4}]^{5}}^{6}
Harley Weston lui répond. 





A derivative problem 
20000604 

Jeff Ellis pose la question : If F(x)=(4+x)(3+2x^{2})^{2}(2+3x^{3})^{3}, find F'(0) Harley Weston lui répond. 





Thearcius Functionius 
20000503 

Kevin Palmer pose la question : With the Olympics fast approaching the networks are focusing in ona new and exciting runner from Greece. Thearcius Functionius has astounded the world with his speed. He has already established new world records in the 100 meter dash and looks to improve on those times at the 2000 Summer Olympics. Thearcius Functionius stands a full 2 meters tall and the networks plan on placing a camera on the ground at some location after the finish line(in his lane) to film the history making run. The camera is set to film him from his knees(0.5 meters up from the ground) to 0.5 meters above his head at the instant he finishes the race. This is a total distance of two meters(the distance shown by the camera's lens). Harley Weston lui répond. 





An indefinite integral 
20000503 

Bonnie Null pose la question : I am to find the indefinite integral of: (e^{x}  e^{x})^{2} dx Claude Tardif lui répond. 





y = x^x^x^x... 
20000405 

Michael Hackman pose la question : Find the derivative of: y = x^x^x^x... on to infinity. Claude Tardif lui répond. 





A mixture problem 
20000306 

Rebecca Edwards pose la question : A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t. Harley Weston lui répond. 





A calculus problem 
19991208 

JT Wilkins pose la question : These are the questions:  Show that there exists a unique function that meets the following requirements:
a) f is differentiable everywhere b) f(0)= f'(0)= 0 c) f(x+y)= f(x)+ f(y), for all real values of x,y  Consider the function F: R>R (All Reals)
F(x) = 0, for x irrational & 1/q, x=p/q gcd(p,q)=1 q > 0 a)determine the values x where f is continuous, respectively discontinuous. b)determine the values x when f is differentiable and for each of these values compute f'(x). Penny Nom lui répond. 





The chain rule 
19991203 

Jennifer Stanley pose la question : This problem is making me dizzy. I would greatly appreciate a little help! Express the derivative dy/dx in terms of x. y=u^2(uu^4)^3 and u=1/x^2 Harley Weston lui répond. 





Two calculus problems 
19991201 

O'Sullivan pose la question : Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help. I've set up a ratio and tried to find the constant but am stuck. Question #2 The figure shows a lamp located three units to the right of the yaxis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (5,0) is on the edge of the shadow, how far above the x axis is the lamp located? The picture shows an x and y axis with only the points 5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5. Harley Weston lui répond. 





Two derivatives 
19991116 

Gina Renicker pose la question : The derivative of: y=e^{(xlnx)} and y=x^{2arctan(x1/2)} Harley Weston lui répond. 





Clockwise or Counterclockwise? 
19991027 

Tim pose la question : A particle moves around the circle x^{2} + y^{2} = 1 with an xvelocity component dx/dt = y  Find dy/dt
 Does the particle travel clockwise or counterclockwise around the circle? Why?
Harley Weston lui répond. 





Derivatives with logs 
19991026 

Kate pose la question : What is the derivative of 5 to the 5x2 at x equals 0.8? Harley Weston lui répond. 





Parametric Equations 
19990806 

Nicholas Lawton pose la question : Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is : yc/p=xp^2cp^3 Harley Weston lui répond. 





A calculus problem 
19990722 

Nicholas Lawton pose la question : The curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the xaxis. the point (0,9) is on the curve. Find the values of p,q and r. Harley Weston lui répond. 





Related rates 
19990513 

Tammy pose la question : The sides of a rectangle increase in such a way that dz/dt=1 and dx/dt=3*dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt? (there is a picture of a rectangle with sides x and y, and they are connected by z, which cuts the rectangle in half) Harley Weston lui répond. 





Graphing the Derivative 
19990118 

Milena Ghebre pose la question : This question has been nagging me for sometime now. Is there a way of finding out the derivative of a function, just by looking at the graph of it? Walter Whiteley lui répond. 





Calculus 
19990116 

Kaylea Rankin pose la question : Differentiate the following. y = 1 /(2+3/x) Jack LeSage and Penny Nom lui répond. 





The area and the circumference of a circle. 
19980827 

Jason Wright pose la question : I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me! Walter Whiteley lui répond. 





A Tightrope Walker. 
19980219 

Amy Zitron pose la question : A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A.... Harley Weston lui répond. 





Mathematical Induction and the Derivative 
19970318 

Shuling Chong pose la question : "Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n." Any educated tries are appreciated. Penny Nom lui répond. 

