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 - Page 146: 36


$f'(\theta) = -36\sin(12\theta)(\cos(12\theta))^2$

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 $u = \cos(12\theta)$ $f(u) = u^3$ Derivate the function: $f'(u) = 3u^2u'$ Now let's find u' $u' = -12\sin(12\theta)$ Then undo the substitution, simplify and get the answer: $f'(\theta) = 3(\cos(12\theta))^2(-12\sin(12\theta))$ $f'(\theta) = -36\sin(12\theta)(\cos(12\theta))^2$
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