## Calculus 10th Edition

Published by Brooks Cole

# Chapter 2 - Differentiation - 2.1 Exercises - Page 103: 13

#### Answer

$-10$

#### Work Step by Step

To find the derivative of a function by the limit process, plug into the formula $f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$: $f'(x)=\lim\limits_{h \to 0}\frac{-10(x+h)-(-10x)}{h}$ Simplify: $f'(x)=\lim\limits_{h \to 0}\frac{-10x-10h+10x}{h}$ $x$- and $h$-values will cancel themselves out: $f'(x)=\lim\limits_{h \to 0}\frac{10h}{h}$ $f'(x)=-10$

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