







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. 





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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





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. 

