   Chapter 9.5, Problem 5E 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 5-8, find the derivative but do not simplify your answer. y =(7 x 6 − 5 x 4 − 2 x 2 − 1 ) (4 x 9 + 3 x 7 − 5 x 2 + 3 x )

To determine

To calculate: The derivative of the function y=(7x65x4+2x21)(4x9+3x75x2+3x) without simplification.

Explanation

Given Information:

The provided function is y=(7x65x4+2x21)(4x9+3x75x2+3x).

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 expression, y=(7x65x4+2x21).(4x9+3x75x2+3x).

Differentiate the provided function with respect to x.

dydx=ddx[(7x65x4+2x21)(4x9+3x75x2+3x)]

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

dydx=(7x65x4+2x21)ddx(4x9+3x75x2+3x)+(4x9+3x75x2+3x)ddx(7x65x4+2x21)

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

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