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

Using termwise division gives $LaTeX: \displaystyle f(x) = - 2 x^{\frac{2}{3}} - 3 x^{\frac{1}{3}} + 3$ . Now the power rule for derivatives can be used instead of the quotient rule. This gives $LaTeX: f'(x) = - \frac{4}{3 \sqrt[3]{x}} - \frac{1}{x^{\frac{2}{3}}}$