Find the derivative $LaTeX: \displaystyle f(x) = \frac{- 5 x^{\frac{7}{3}} - 4 x^{\frac{4}{3}} + 5 x^{\frac{1}{3}}}{x^{\frac{1}{3}}}$

Using termwise division gives $LaTeX: \displaystyle f(x) = - 5 x^{2} - 4 x + 5$ . Now the power rule for derivatives can be used instead of the quotient rule. This gives LaTeX: f'(x) = - 10 x - 4