Find the derivative $LaTeX: \displaystyle f(x) = \frac{- 5 x^{\frac{9}{4}} - 4 x^{\frac{5}{4}} - 5 x^{\frac{1}{4}}}{x^{\frac{1}{4}}}$

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