Find the derivative $LaTeX: \displaystyle f(x) = \frac{3 x^{\frac{5}{2}} - 3 x^{\frac{3}{2}} + 2 x^{\frac{1}{2}}}{x^{\frac{1}{2}}}$

Using termwise division gives $LaTeX: \displaystyle f(x) = 3 x^{2} - 3 x + 2$ . Now the power rule for derivatives can be used instead of the quotient rule. This gives LaTeX: f'(x) = 6 x - 3