Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 22



Work Step by Step

Using the chain rule for derivatives, the derivative of a composition of functions $f(g(x))$ is equal to $f'(g(x)) \times g'(x)$. Using this technique leaves $\frac{1}{cos(x)} \times -sin(x)=-\frac{sin(x)}{cos(x)}=\boxed{-\tan(x)}$.
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