volume of a cube versus side length

[emma3001]

Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.

I know that surface area= 6l^2(because of the six faces)
I know that volume is l^3. How do I relate volume then to edge length

[Pere Callahan]

Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of a cube.



The "rate of change" is the derivative.

So what is the derivative of the volume with respect to the edge length?

[emma3001]

Thanks! I now realize that the first derivative of the volume is 3l^2, which is half the surface area

[Pere Callahan]

Right.