Derivative of the Area of a Circle

[husky88]

Homework Statement

Show that the rate of change of the area of a circle with respect to its radius is the same as the circumference of the circle. Can you suggest why?

Homework Equations

A = \pir^{2} = f(r)
L = 2\pir = g(r)

The Attempt at a Solution

I have showed that the derivative of f(r) is equal to g(r).
But I have no idea why the area and the circumference of the circle are related in such a way. Any suggestions greatly appreciated.
Thank you.

 

[Quisquis]

Start by thinking about what any derivative of a function is describing in general, and then how it applies here specifically.

 

[husky88]

The derivative describes the slope of a tangent to the circle which is perpendicular to the radius... but I don't seem to go anywhere from here... hmmm