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.
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
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