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

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