Calculus, 10th Edition (Anton)

by Anton, Howard

Published by Wiley

ISBN 10: 0-47064-772-8

ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 152: 35

Answer

The statement is false.

Work Step by Step

We will find the derivative using the Chain Rule: $$g'(x)=(f(x)\sin x)'=f'(x)\cdot\sin x+f(x)\cdot(\sin x)'= f'(x)\sin x+f(x)\cos(x)\neq f'(x)\cos x$$ So, the statement is false.

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