$\displaystyle AC=\frac{TC}{x}=\frac{2000}{x}+20+\frac{10}{\sqrt{ x}}$

So i have to show that there is no minimum.

thus i have to differentiate the function, which apparently gives this

$\displaystyle \frac{dAC}{dx}=AC'= -\frac{2000}{x^2}-\frac{5}{\sqrt[3]{}x^3}$

I don't know how they got that answer , can someone please explain?