   Chapter 9.5, Problem 19E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 11-20, find the indicated derivatives and simplify. y '  for  y = x ( x 2 + 4 ) x − 2

To determine

To calculate: The derivative of the expression x(x2+4)x2 with simplification.

Explanation

Given Information:

The provided expression is x(x2+4)x2.

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.

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

ddx(f.g)=f.dgdx+g.dfdx

Calculation:

Consider the provided expression x(x2+4)x2,

Multiply the numerator in order to apply the quotient rule:

x(x2+4)=x3+4x

For the derivative of x3+4xx2, follow the steps:

In the expression, the value of,

f(x)=x3+4x

And

g(x)=x2

Apply the quotient rule of the expression,

ddx(fg)=ddx(x3+4x).(x2)ddx(x2).(x3+4x)(x2)2

Evaluate the expression further,

ddx(fg)=(ddx(x3)+4ddx(x))

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