Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises: 39

Answer

$f'(\theta) = (1 - \sin \theta)\sec ^2 (\theta + \cos \theta)$

Work Step by Step

In order to derivate this function you have to apply the chain rule Let's make an «u» substitution to make it easier $u = \theta + \cos \theta $ $f(u) = \tan u$ Derivate the function: $f'(u) = \sec ^2 u$ Now let's find u' $u' = 1 - \sin \theta$ Then undo the substitution, simplify and get the answer: $f'(\theta) = (1 - \sin \theta)\sec ^2 (\theta + \cos \theta)$
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