Answer
$f'(x) = \dfrac{5}{2}x^{3/2}-2x^{-1/2}$
Work Step by Step
In order to derivate this function you have to apply the power rule:
$\dfrac{d}{dx}(x^n)=nx^{n-1}$
But first let's rewrite the function
$f(x) = \dfrac{x^3}{x^{1/2}}-\dfrac{4x}{x^{1/2}}$
$f(x) = x^{5/2}-4x^{1/2}$
then
$f'(x) = \dfrac{5}{2}x^{3/2}-2x^{-1/2}$
