system
Given the following post, respond as if you're commenting on Reddit:
human
Is the formula for perimeter of circle a derivative of the fomula for area of circle?

d/dr [пr^(2)] = 2пr

Can someone explain this in terms of physics or practice?

Thanks.
gpt
If you increase the radius of a circle a small amount, its area increases by adding a thin strip around the outside. If you "unroll" this circular strip to make it straight, you can see that its area is equal to the small change in radius times the circumference of the circle. Hence dA = C*dr, or dA/dr = C.