Calculus (3rd Edition)

$$f'(x)= \frac{27}{2}x^{3/2}+\frac{2}{x^2}.$$
First, we simplify $f(x)$ as follows $$f(x)=\frac{9x^{5/2}-2}{x}=9x^{3/2}-2x^{-1}.$$ Now, the derivative is given by $$f'(x)=9(3/2)x^{1/2}+2x^{-2}=\frac{27}{2}x^{3/2}+\frac{2}{x^2}.$$