   Chapter 9.5, Problem 7E ### 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 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)(x32x2+5).

Formula Used:

The product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fdgdx+gdfdx.

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

The simple power rule of derivative ddx(xn)=nxn1.

Calculation:

Consider the provided function, y=(x2+x+1)(x32x2+5).

Differentiate the provided function with respect to x.

dydx=ddx[(x2+x+1)(x32x2+5)]

Use the product rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=fdgdx+gdfdx.

dydx=(x2+x+1)ddx(x32x2+5)+(x32x2+5)ddx(x2+x+1)=(x2+x+1)(ddx(x3)2ddx(x2)+ddx(5))+(x32x2+5)(ddx(x2)+ddx(x)+ddx(1))

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

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