Given: A=pi(r)^2, find dA/dr using first principle in Derivative.

Look at the two I've done here: 

http://web2.0calc.com/questions/what-is-the-derivative-of-y-3-sqrt-2x-1-using-the-first-principle

http://web2.0calc.com/questions/what-is-the-derivative-of-y-4sqrt-x-using-the-first-principle

and see if you can use a similar approach (this should be easier than those as you won't need to use a Taylor series expansion).