how to differentiate A=4x^2 + 216/x? I got stuck at 216/x?

\frac{1}{x} = x^{-1}

therefore:

4x^2 + \frac{216}{x} = 4x^2 + 216x^{-1}

Go from there

\frac{1}{x} = x^{-1}

therefore:

4x^2 + \frac{216}{x} = 4x^2 + 216x^{-1}

Go from there

so, it will be 8x - 216x^-2?

the full question is given a rectangular ( 2x by x by x)
the volume is 72cm3.
the total surface area is A=4x^2 + 216/x.
find the minimum value of the total surface area?

i don't know how to start.

so, it will be 8x - 216x^-2?

the full question is given a rectangular ( 2x by x by x)
the volume is 72cm3.
the total surface area is A=4x^2 + 216/x.
find the minimum value of the total surface area?

i dont know how to start.

That's right, so now you know that when dA/dx is 0, A is either at a maximum, minimum, or a reflex point. To find out which, you can look at d^2A/dx^2 , which should be positive for a minimum.

And solve for dA/dx = 0