Question

What will be dr/dA if A=(pi)(r)^2

Answer 1

Thanks a million!

Answer 2

Let's rewrite that as r=sqrt(A/pi)=A^(1/2)/sqrt(pi): dr/dA=1/[2sqrt(A)*sqrt(pi)]
that's 1/[2*sqrt(pi*A)]

Answer 3

We need to differentiate with respect to A. Therefore, we need to rewrite the equation in terms of A. This becomes \[A = \pi r^2 \rightarrow r = \sqrt{A \over \pi}\]Taking the derivative\[{dr \over dA} = \left(1 \over 2 \right) \sqrt{ 1 \over \pi A}\]

Answer 4

But Dryanni, I tried the same method as yours first and I seemed to get the wrong answer. Jimmyrep's has worked somehow. And the one by eashmore gets the same answer in the end as well...Seems you're on the same page as me..

Answer 5

My bad. I did retract myself in rereading Jimmy's. The only difference is the choice of variable. They are all correct but I would side with having the independent variable in the equation.

Answer 6

in terms of A
dr/dA = 1 / 2sqrt(piA)

Answer 7

But what about your first answer then, isn't it suitable?

Answer 8

i only half did the problem - i meant to to substitute r = sqrt(A/pi) into my answer
my answer was not strictly correct

Answer 9

Thanks a LOT - you made everything a lot clearer! Cheers!

Answer 10

yw

Answer 11

sorry for my oversight