Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 141: 62


$$f'(x)=-\frac{1}{(3-x)^2}$$ $$f''(x)=\frac{2}{(3-x)^3}$$

Work Step by Step

$$f(x)=\frac{1}{3-x}=(3-x)^{-1}$$ Differentiating with respect to $x$, using power rule, $$f'(x)=-1(3-x)^{-2}=-\frac{1}{(3-x)^2}$$ Differentiating again with respect to $x$, using power rule, $$f''(x)=(-1)(-2)(3-x)^{-3}=\frac{2}{(3-x)^3}$$.
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