Chapter 9.5, Problem 4E

### 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 1-4, find the derivative and simplify. f ( x ) = ( x 12 + 3 x 4 + 4 ) ( 2 x 3 − 1 )

To determine

To calculate: The derivative of the function f(x)=(x12+3x4+4)(2x31) with simplification.

Explanation

Given Information:

The provided function is f(x)=(x12+3x4+4)â‹…(2x3âˆ’1).

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 f(x)=(x12+3x4+4)â‹…(2x3âˆ’1).

Differentiate the provided function with respect to x.

ddx[f(x)]=ddx[(x12+3x4+4)â‹…(2x3âˆ’1)]

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

ddx[f(x)]=(x12+3x4+4)ddx(2x3âˆ’1)+(2x3âˆ’1)ddx(x12+3x4+4)

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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