Calculus, 10th Edition (Anton)

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: 36


The statement is true.

Work Step by Step

First we will find the derivative using the Chain Rule: $$g'(x)=(f(x)\sin x)'=f'(x)\sin x+f(x)(\sin x)'=f'(x)\sin x+f(x)\cos x$$ Now we will evaluate $g'(x)$ for $x=0$: $$g'(0)=f'(0)\sin0+f(0)\cos0=f'(0)\cdot0+f(0)\cdot1=f(0)$$ So, the statement is true.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.