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

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