Author Question: What is the second derivative of the area of a circle with respect to r? (Read 2977 times)

hummingbird · **on:** Jun 19, 2013

I know it would come out to 2pi, but what does that mean? The first derivative is circumference, but what is the second derivative?

Millan · **Reply #1 on:** Jun 19, 2013

The second derivative would be the number of radians in a circle. 2pi radians is the same as 360 degrees.

federox · **Reply #2 on:** Jun 19, 2013

so we have the Area (in units squared)
when taken we get the Circumference =A';
A" is a constant...
You have successfully reached the end of the chain...
P'=V
V'=A
A=J... but eventually you'll work it down to a constant as well...
2pi alone doesn't really mean anything.

curlz · **Reply #3 on:** Jun 19, 2013

y = pi*(r^2)
y' = pi * (2r) - pi is constant
y' = 2pi * r - you're right it's the circumference
y'' = 2pi

I think this is the difference in the circumference when the radius increased by 1....