Find the derivative $LaTeX: \displaystyle f(x) = \frac{x^{\frac{3}{5}} - 3 x^{\frac{2}{5}} - 4 x^{\frac{1}{5}}}{x^{\frac{1}{5}}}$

Using termwise division gives $LaTeX: \displaystyle f(x) = x^{\frac{2}{5}} - 3 x^{\frac{1}{5}} - 4$ . Now the power rule for derivatives can be used instead of the quotient rule. This gives $LaTeX: f'(x) = \frac{2}{5 x^{\frac{3}{5}}} - \frac{3}{5 x^{\frac{4}{5}}}$