Chapter 9.6, 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

# Differentiate the functions in Problems 3-20. h ( x ) = 3 4 ( x 5 − 2 x 3 + 5 ) 8

To determine

To calculate: The derivative of the function h(x)=34(x52x3+5)8.

Explanation

Given Information:

The provided function is h(x)=34(x5âˆ’2x3+5)8.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nunâˆ’1â‹…dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is fâ€²(x)=nxnâˆ’1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

Calculation:

Consider the function,

h(x)=34(x5âˆ’2x3+5)8

Consider (x5âˆ’2x3+5) to be u,

h(x)=34u8

Differentiate both sides with respect to x,

hâ€²(x)=ddx(34u8)=34ddx(u8)

Use the power rule,

hâ€²(x)=34â‹…8u8âˆ’1â‹…dudx=3â‹…2u7dudx=6u7dudx

Substitute (

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