Chapter 9.5, Problem 8E

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# In Problems 5-8, find the derivative but do not simplify your answer. y =( x 2 + x + 1 )( x 3 − 2 x + 5 )

To determine

To calculate: The derivative of the function y=(x2+x+1)(x32x2+5) without simplification.

Explanation

Given Information:

The function is y=(x2+x+1)(x3âˆ’2x2+5).

Formula Used:

The product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fâ‹…dgdx+gâ‹…dfdx.

The sum and difference rule of derivate of functions, ddx[u(x)Â±v(x)]=ddxu(x)Â±ddxv(x).

The simple power rule of derivative ddx(xn)=nxnâˆ’1.

Calculation:

Consider the provided function, y=(x2+x+1)(x3âˆ’2x2+5).

Differentiate the provided function with respect to x.

dydx=ddx[(x2+x+1)(x3âˆ’2x2+5)]

Use the product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fâ‹…dgdx+gâ‹…dfdx.

dydx=(x2+x+1)ddx(x3âˆ’2x2+5)+(x3âˆ’2x2+5)ddx(x2+x+1)=(x2+x+1)(ddx(x3)âˆ’2ddx(x2)+ddx(5))+(x3âˆ’2x2+5)(ddx(x2)+ddx(x)+ddx(1))

Use the sum and difference rule of derivate of functions, ddx[u(x)Â±v(x)]=ddxu(x)Â±ddxv(x)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started