Find the derivative of volume of a sphere.
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.