Hey, I'm doing some homework and I'm a little confused with this question.

Find the rate of change of the volume V of a cube with respect to

(a) the length w of a diagonal on one of the faces.

(b) the length z of the one of the diagonals of the cube.

So i'm trying to find $\displaystyle \frac{dv}{dw} $

I know that the Volume of a cube is $\displaystyle v=x^3 $

What i need to do is find a way of expressing V in terms of w.

I know that $\displaystyle x^2 + x^2 = w^2 $ and solving for x I get $\displaystyle x= \frac{w}{2} $. Unless my math is incorrect (which is very possible).

The next step is the plug that into $\displaystyle v=x^3 $ so i get $\displaystyle v=(\frac{w}{2})^3 $

Do i just find the derivative of that to get answer? I know that's wrong somewhere since the answer is $\displaystyle (\frac{3 (2^(\frac{1}{2})}{4})w^2 $

Can anyone tell me what i'm doing wrong? thank you very much