Answer
$\frac{15}{2}x^{3/2}-\frac{3}{2}x^{1/2}-x^{-3/2}$
Work Step by Step
Using the quotient rule, we have
$f'(x)=\frac{\sqrt {x}\frac{d}{dx}(3x^{3}-x^{2}+2)-(3x^{3}-x^{2}+2)\frac{d}{dx}(\sqrt {x})}{(\sqrt {x})^{2}}$
$=\frac{\sqrt {x}(9x^{2}-2x)-(3x^{3}-x^{2}+2)\frac{1}{2\sqrt {x}}}{x}$
$=\frac{9x^{5/2}-2x^{3/2}-\frac{3x^{5/2}}{2}+\frac{x^{3/2}}{2}-x^{-1/2}}{x}$
$=\frac{15x^{5/2}}{2x}-\frac{3x^{3/2}}{2x}-\frac{x^{-1/2}}{x}$
$=\frac{15}{2}x^{3/2}-\frac{3}{2}x^{1/2}-x^{-3/2}$
