Chapter 3 - Derivatives - 3.4 The Product and Quotient Rules - 3.4 Exercises - Page 160: 4

Quotient Rule: $f(x) = \frac{1}{x^{10}}$ $f'(x) = \frac{(0)(x^{10})-(1)(10x^{9})}{(x^{10})^2} = \frac{-10}{10^{11}}$ Power Rule: $f(x) = \frac{1}{x^{10}} = x^{-10}$ $f'(x) = (-10)x^{-10-1} = -10x^{-11}$

Derivatives can be taken in many ways. As long as a function follows the general form of a particular method, that method can be utilized. In this case, the quotient and power rules are applicable.