   Chapter 9.5, Problem 1CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# True or false: The derivative of the product of two functions is equal to the product of the derivatives of the two functions.

To determine

Whether the statement ‘The derivative of the product of the two functions is equal to the product of the derivatives of the two functions” is true or false.’

Explanation

Consider two function f(x) and g(x).

Let f(x)=x2 and g(x)=2x2.

The derivative of the function f(x), use the simple power rule of derivative ddx(xn)=nxn1.

ddx(f(x))=ddx(x2)=2x21=2x

The derivative of the function g(x), use the simple power rule of derivative ddx(xn)=nxn1.

ddx(f(x))=ddx(2x2)=2(2x21)=4x

The product of the derivative of functions f(x) and g(x).

(ddx(f(x)))(ddx(g(x)))=(ddx(x2))⋅<

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