Chapter 9.5, Problem 5E

### 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 =(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=(7x6âˆ’5x4+2x2âˆ’1)â‹…(4x9+3x7âˆ’5x2+3x).

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 expression, y=(7x6âˆ’5x4+2x2âˆ’1).(4x9+3x7âˆ’5x2+3x).

Differentiate the provided function with respect to x.

dydx=ddx[(7x6âˆ’5x4+2x2âˆ’1)â‹…(4x9+3x7âˆ’5x2+3x)]

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

dydx=(7x6âˆ’5x4+2x2âˆ’1)ddx(4x9+3x7âˆ’5x2+3x)+(4x9+3x7âˆ’5x2+3x)ddx(7x6âˆ’5x4+2x2âˆ’1)

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

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