







Derivées partielle 
19991019 

Arnaud Flandin pose la question : Quel est la definition des derivées partielle 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. 





Heat equation 
20171123 

Max pose la question : What does du\dt=a(triangle)^2u mean. Can it be solved for t. Penny Nom lui répond. 





A tangent to a curve 
20171022 

Jasem pose la question :
Suppose that
f(x)=(3x3)^1/2.
(A) Find an equation for the tangent line to the graph of f(x) at x=2
(B) Find all values of xx where the tangent line is horizontal, and enter them as a commaseparated list (e.g., 2,3,6). If there are none, enter none.
Values of 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. 





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. 





The derivative of x! 
20160416 

Sang pose la question : How to find the derivative of x! and integral of x! 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. 





Constructing a box of maximum volume 
20150414 

Margot pose la question : I need to do a PA for maths and I'm a bit stuck.
The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up.
8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z. 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. 





The derivative of sin(x) 
20140426 

Lucky pose la question : f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem. Penny Nom lui répond. 





The domain of a derivative 
20131010 

Renee pose la question : I am looking to find the domain of a derivative of a radical function,
one such as: f(x) = the square root of (8 − x).
I am kind of unclear on how domains work for derivative.
I don't understand how you take a function's domain and use that to
find the derivative's domain.
Thanks! Penny Nom lui répond. 





Equal ordinate and abscissa 
20130815 

sonit pose la question : the slope of tangent to the curve y=(4x^2)^1/2 at the point, where the ordinate and abscissa are equal, is Penny Nom lui répond. 





Distance as a function of acceleration 
20130710 

Tom pose la question : If you start at a stoplight and your acceleration is 16t  t^2, how far have you gone after 8 seconds? 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 derivative of y = sin (30º + x) 
20121107 

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





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. 





An antiderivative of the square root of (8t + 3) 
20110419 

Caitlyn pose la question : I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem.
What's the antiderivative of the square root of (8t + 3)
~Caitlyn= Penny Nom lui répond. 





A stone is dropped into a lake 
20110324 

AnneMarie pose la question : A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 25 cm/s. Find the rate at which the area within the circle is increasing after 4s. Penny Nom lui répond. 





The integral of (x^2*exp(x)/(exp(x)1)^2 
20100809 

sujoy pose la question : please find this integral for me
int(x^2*exp(x)/(exp(x)1)^2 Robert Dawson lui répond. 





Using the limit definition 
20100606 

Meagan pose la question : Using the limit definition find the derivative of 3/(2x^2) Harley Weston lui répond. 





The derivative of y=x^x 
20100409 

David pose la question : So, its David, and I was wondering about the derivative of y=x^x. I have often seen it be shown as x^x(ln(x)+1), but when I did it through limits it turned out differently. Here's what I did:
It is commonly know that df(x)/dx of a function is also the limit as h>0 of f(x+h)f(x)/h.
To do this for x^x you have to start with lim h>0 ((x+h)^(x+h)x^x)/h. The binomial theorem then shows us that this is equal to lim h>0 (x^(x+h)+(x+h)x^(x+h1)h+...x^x)/h
This is also equal to lim a>0 lim h>0 (x^(x+a)+(x+h)x^(x+h1)h...x^x)/h.
Evaluating for a=0 you get lim h>0 (x^x+(x+h)x^(x+h1)h...x^x)/h
Seeing as the last 2 terms on the numerator cancel out you can simplify to a numerator with h's is each of the terms, which you can then divide by h to get:
lim h>0 (x+h)x^(x+h1)... which when evaluated for h=0 gives us: x(x^(x1)). This statement is also equal to x^x.
This contradicts the definition of the derivative of x^x that is commonly shown. So, my question is: can you find any flaws in the logic of that procedure? I do not want to be shown how to differentiate x^x implicitly because I already know how to do that. Robert Dawson 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 second derivative of y = x³ (x² + 5) 
20091214 

Kyrie pose la question : Find d²y/dx² for this function:
y = x³ (x² + 5) Penny Nom lui répond. 





Graphing y=(4x^2)^5 
20091025 

natalie pose la question : I want to graph the curve of y=(4x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8.
Thank you so much,
natalie Harley Weston 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. 





An antiderivative problem 
20090813 

Indrajit pose la question : ∫4e^x + 6e^x/(9e^x + 4e^x)dx = Ax + Bloge(9e2x  4) + C
then A=?......B=?.....C=?
plz solve it...."^" stands for "to the power of".... Harley Weston lui répond. 





Application of Derivatives of Trig Functions 
20090521 

Alannah pose la question : I have a word problem from my Calculus textbook that I can't figure out.
Triangle ABC is inscribed in a semicircle with diameter BC=10cm. Find the value of angle B that produces the triangle of maximum area.
I am supposed to set up an equation for the area of the triangle A=b x h/2 using Trig functions based on angle B to represent the base and height but I'm not sure how to do this when the side length given is not the hypotenuse. Janice Cotcher lui répond. 





The derivative using limits 
20090421 

Kirstin pose la question : I am trying to take the limit of f(x) = [f(x+h)f(x)] / h
If you try taking the limit by substituting the limiting value h=0, you get 0/0,
which of course is not the right answer. You rewrite f(x+h)f(x) so it has a factor
of h in it, which you cancel with the h in the denominator before you substitute h=0.
But I am not sure how to do this. Thanks. Robert Dawson lui répond. 





The second derivative of h(x)=f(g(x)) 
20090216 

Kristina pose la question : If h(x)=f(g(x)), and is differentiable, then find h"(x). Robert Dawson lui répond. 





A definite integral 
20090209 

Mathata pose la question : Evaluate: integral from 0 to 1, x^2 e^x^3dx Harley Weston 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. 





Partial derivatives 
20090117 

Meghan pose la question : I have a question I've been working at for a while with maxima/minima of partial derivatives.
"Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed.
Find the dimensions of the rectangular package of greatest volume that can be mailed.
(84 = length + girth = l + 2x + 2y)" Harley Weston lui répond. 





Negative rate of change 
20090112 

hemanshu pose la question : when i have to find rate of change of decrease in any value my ans comes in negative why?????????? Penny Nom 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. 





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. 





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. 





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. 





f(x) =ax^blnx 
20080413 

charles pose la question : supposef(x) =ax^blnx is a real valued function. Determine exact values(not decimal approximations) fro nonzero constants a and b so that the function f has a critical point at x=e^3 and a maximum value of 1/2e 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. 





A curve sketch 
20071122 

Ahson pose la question : Find critical points, determine the monotonicity and concavity and sketch
a graph of f(x) with any local maximum, local minimum and inflection
points labeled:
1. f(x) = x^4  x^3  3x^2 + 1 Harley Weston 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. 





How to solve related rates problems 
20071027 

David pose la question : Can you plz explain how and where you come up with an equation to solve this?
Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second. Stephen La Rocque 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. 





Using the chain rule to solve a derivative 
20070729 

Charles pose la question : I need to find the derivative fo the following function.
_______________________
\/ ______________
\/ (x  1) / (x + 2) + 1 Stephen La Rocque 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. 





Derivative of a Function 
20070709 

Bob pose la question : What is the derivative of the function a sub n = [n/(n+1)]^n ? Stephen La Rocque lui répond. 





Log base 2 of log base 2 of x 
20070627 

alex pose la question : y = log base 2 of lag base 2 of x
The slope of the tangent to the given curve at its xintercept is..? Harley Weston lui répond. 





Maximizing the volume of a cone given the slant length 
20070514 

Christina pose la question : A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised. Stephen La Rocque and Kerstin Voigt 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. 





y = sin(2x) 
20070322 

bader pose la question : sin(2x)
find dx/dy 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. 





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. 





livinia the housefly finds herself caught in the oven 
20060627 

Danielle pose la question :
livinia the housefly finds herself caught in the oven at the point (0,0,1). the temperature at the points in the oven is given by the function
T(x,y,z) = 10 (xe^{(y2)} + ze^{(x2)})
where the units are in degrees celsius.
(i.)so if livinia begins to move towards the point (2,3,1) at what rate in deg/cm does she find the temp. changing?
(ii.)in what direction should she move in order to cool off as rapidly as possible?
(iii.)suppose that livinia can fly at a speed of the square root of 2 (cm/sec.) if she moves in the direction of part (ii) at what rate will she find the temp. to be changing?
Penny Nom 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. 





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

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





The third derivative 
20041015 

Holly pose la question : Why would you ever take the third derivative? Harley Weston lui répond. 





differentiate Y=X^X^X 
20040913 

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





Areas, perimeters and derivatives 
20040215 

Geoff pose la question : A recent lecture in my calculus class led me to realize that the derivative of the area of a circle, with respect to the radius is equal to the circumfrence. This also holds true for the relationship between the volume of a sphere and the surface area of that sphere:
why do these hold true? why is it only for circular objects? 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. 





Functions, graphs and derivatives 
20031005 

Jathiyah pose la question : I wanted to know how would you tell (on a graph diplaying two funtions), which funtion is the derivative of the other? Walter Whiteley 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. 





The slope of a tangent line 
20020304 

Ridley pose la question : Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). 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. 





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. 





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. 





Concavity 
20001022 

Alex pose la question : the question is: on what interval is f(x)=(x^{2})(e^{x})? ive found the 2nd derivative which is e^{x}(x^{2}+4x+2) and i did the quadratic to get 22^{0.5} and 2+2^{0.5}, but i dont know what the interval is. Harley Weston 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 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. 





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. 

