# ( f ( x ) g ( x ))′ = f′ ( x ) g ′( x ).

### Study Guide for Stewart's Single V...

8th Edition
Stewart + 3 others
Publisher: Cengage Learning
ISBN: 9781305279148

### Study Guide for Stewart's Single V...

8th Edition
Stewart + 3 others
Publisher: Cengage Learning
ISBN: 9781305279148

#### Solutions

Chapter
Section
Chapter 3.2, Problem 1PT
Textbook Problem

## (f(x)g(x))′ = f′(x)g′(x).

Expert Solution
To determine

Whether the statement “[f(x)g(x)]=f(x)g(x)” is true or false.

### Explanation of Solution

Formula used:

General Power Rule:

For any real numbers n, the derivative of the function f(x)=xn is f(x)=nxn1 or ddx(xn)=nxn1.

Product Rule:

If f and g are differentiable, then [f(x)g(x)]=f(x)g(x)+f(x)g(x).

Calculation:

Check whether the statement [f(x)g(x)]=f(x)g(x) is true or false as follows.

From the above product rule, it is clear that [f(x)g(x)]=f(x)g(x)+f(x)g(x).

That is, [f(x)g(x)]f(x)g(x).

Counter Example:

Consider, f(x)=6x4 and g(x)=x+2 to check [f(x)g(x)]=f(x)g(x).

Compute [f(x)g(x)] by using product rule mentioned above

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