   Chapter 9.5, Problem 6E ### 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 =(9 x 9 − 7 x 7 − 6 x )(3 x 5 − 4 x 4 + 3 x 3 − 8 )

To determine

To calculate: The derivative of the function y=(9x97x76x)(3x54x4+3x38) without simplification.

Explanation

Given Information:

The provided function is y=(9x97x76x)(3x54x4+3x38).

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=(9x97x76x)(3x54x4+3x38),

Differentiate the provided function with respect to x.

dydx=ddx[(9x97x76x)(3x54x4+3x38)]

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

dydx=(9x97x76x)ddx(3x54x4+3x38)+(3x54x4+3x38)ddx(9x97x76x)=(9x97x76x).(ddx(3x5)4ddx(x4)+3ddx(x3)ddx(8))+(3x54x4+3x38).(9ddx(x9)7ddx(x7)6ddx(x))

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

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