   Chapter 9.5, Problem 20E ### 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

# In Problems 11-20, find the indicated derivatives and simplify. f ' ( x )  for  f ( x ) = ( x + 1 ) ( x − 2 ) x 2 + 1

To determine

To calculate: The derivative of the expression (x+1)(x2)x2+1 with simplification.

Explanation

Given Information:

The provided expression is (x+1)(x2)x2+1.

Formula Used:

As per the quotient rule, if two functions are given in the form f(x)g(x), then the derivative is given as:

ddx(fg)=f.gg.fg2

Calculation:

Consider the provided expression (x+1)(x2)x2+1.

Multiply the numerator in order to apply the quotient rule:

(x+1)(x2)=x(x2)+1(x2)=x22x+x2=x2x2

For the derivative of x2x2x2+1, follow the steps:

In the expression, the value of,

f(x)=x2x2

And

g(x)=x2+1

Apply the quotient rule of the expression,

ddx(fg)=ddx(x2x2).(x2+1)ddx(x2+1).(x2x2)(x2+1)2

Evaluate the expression further,

ddx(fg)=(ddx(x2)ddx(x)ddx(2))

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