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
I know that the Volume of a cube is
What i need to do is find a way of expressing V in terms of w.
I know that and solving for x I get . Unless my math is incorrect (which is very possible).
The next step is the plug that into so i get
Do i just find the derivative of that to get answer? I know that's wrong somewhere since the answer is
Can anyone tell me what i'm doing wrong? thank you very much