   Chapter 9, Problem 72RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

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)=1x34x.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nun1dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

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

Calculation:

Consider the function, g(x)=1x34x

Consider (x34x) to be u,

g(x)=1u=1u12=u12

Differentiate both sides with respect to x,

g(x)=ddx(u12)

Use the power of x rule,

g(x)=12u121dudx=12u3/2dudx

Substitute (x3

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Describe the set of points (x,y) such that x2+y2=9.

Finite Mathematics and Applied Calculus (MindTap Course List)

Perform the indicated operation for the following. 8.

Contemporary Mathematics for Business & Consumers

If f(x) = g(x) for 0 x 1, then f(x) = g(x) for 0 x 1.

Single Variable Calculus: Early Transcendentals

Find for x = 3t2 + 1, y = t6 + 6t5. t4 + 5t3 4t3 + 15t2

Study Guide for Stewart's Multivariable Calculus, 8th 