Calculus 10th Edition

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

Chapter 2 - Differentiation - Review Exercises: 4

Answer

$-6x^{-2}$

Work Step by Step

$f(x)=\frac{6}{x}$ $f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{(\frac{6}{x+h})-{(\frac{6}{x}})}{h}=\lim\limits_{h \to 0}\frac{(\frac{6x-6(x+h)}{x^2+hx})}{h}=\lim\limits_{h \to 0}\frac{-6h}{h(x^2+hx)}=\lim\limits_{h \to 0}\frac{-6}{x^2+hx}=\frac{-6}{x^2}$$$=-6x^{-2}$$
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