Chapter 9, Problem 72RE

### 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

# 72.  Find  g ' ( x )  if  g ( x ) = 1 x 3 − 4 x .

To determine

To calculate: The value of g(x) for the function g(x)=1x34x.

Explanation

Given Information:

The provided function is g(x)=1x3âˆ’4x.

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, g(x)=1x3âˆ’4x

Consider (x3âˆ’4x) to be u,

g(x)=1u=1u12=uâˆ’12

Differentiate both sides with respect to x,

gâ€²(x)=ddx(uâˆ’12)

Use the power of x rule,

gâ€²(x)=âˆ’12â‹…uâˆ’12âˆ’1â‹…dudx=âˆ’12uâˆ’3/2dudx

Substitute (x3

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