Chapter 9.5, Problem 7E

### 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 5 − 2 x 4 +1)( x 3 − 5 x − 7 )

To determine

To calculate: The derivative of the function y=(x52x4+1)(x35x7) without simplification.

Explanation

Given Information:

The function is y=(x5âˆ’2x4+1)(x3âˆ’5xâˆ’7).

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=(x5âˆ’2x4+1)(x3âˆ’5xâˆ’7)

Differentiate the provided function with respect to x.

dydx=ddx[(x5âˆ’2x4+1)(x3âˆ’5xâˆ’7)]

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

dydx=(x5âˆ’2x4+1)ddx(x3âˆ’5xâˆ’7)+(x3âˆ’5xâˆ’7)ddx(x5âˆ’2x4+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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