# Derivative Question

peacemaster

## Homework Statement

Find the derivative of volume of a sphere.

## Homework Equations

Volume=4/3 * pi * r^3

OR Volume = 4/3 * pi * (c/2pi)^3 where c=circumference

## The Attempt at a Solution

This is where I have had some serious trouble. Allow me to explain.

Obviously the derivative is 4pi*r^2

but look what happens when I use r=circumference/2pi

I get a totally different answer. Then the derivative is (c^2)/(2pi^2)

I do not understand why I should get two different answers for the derivative of volume depending only on when I choose to substitute c/2pi for the r value. I would really appreciate it if somebody could help shed some light on what I am doing wrong.

Thanks,

Sean

Homework Helper
Hi Sean!

Hint: chain rule

peacemaster
ok, could you elaborate on that a little. I know what the chain rule is but I don't see it's application here. The result ought to be the same regardless of when I plug in the value of the radius (in this case c/2pi). I don't see why the value of the radius would ever change. That seems like it should remain the same regardless of when i plug it in.

peacemaster
Also, where would apply the chain rule here? I don't see it.

peacemaster
Oh, I see it now. Thanks.