Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

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



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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