## Calculus, 10th Edition (Anton)

Published by Wiley

# Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 152: 36

#### Answer

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.

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