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: 23


$y' = -\dfrac{\sin(\ln x)}{x}$

Work Step by Step

In order to derivate this function you have to apply the chain rule Let's make a «u» substitution to make it easier $f(u) = \cos(u)$ $u =\ln x$ Derivate the function: $f'(u) = -u' \sin(u)$ Now let's find u' $u' = \dfrac{1}{x}$ Then undo the substitution, simplify and get the answer: $y' = -\dfrac{\sin(\ln x)}{x}$
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