Chapter 2 - The Derivative - 2.4 The Product And Quotient Rules - Exercises Set 2.4 - Page 147: 17

$f'x=-5x^{-5}-9x^{-4}-4x^{-3}-7x^{-2}+14$

Rewrite the function $f(x)=(2x+1)(1+\frac{1}{x})(x^{-3}+7)$ $f(x)=(2x+1+2+x^{-1})(x^{-3}+7)$ $=(2x+3+x^{-1})(x^{-3}+7)$ $=2x^{-2}+3x^{-3}+x^{-4}+14x+21+7x^{-1}$ Evaluate $f'(x)$ $f'(x)=(2x^{-2}+3x^{-3}+x^{-4}+14x+21+7x^{-1})'$ $=-4x^{-3}-9x^{-4}-5x^{-5}+14+0-7x^{-2}$ $=-5x^{-5}-9x^{-4}-4x^{-3}-7x^{-2}+14$