Calculus 8th Edition

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

Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises - Page 158: 3


$f'(u) = \pi sec^2(\pi x)$

Work Step by Step

First write $f(g(x))$ in terms of $u$ and $f(u)$. Original expression: $y = tan(\pi x)$ $u = g(x) = \pi x$ $y = f(u) = tan(u)$ Apply the chain rule to find the derivative: $f'(g(x)) \times g'(x) $ = > $f'(u) \times u'$ => $\frac{dy}{du}tan(u) \times\frac{du}{dx}(\pi x) $ Derive (Note: $\pi $ is a constant and is moved to the outside of the derivative of $u$) $sec^2(u)\times \pi$ $\pi sec^2(\pi x)$
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