   Chapter 9.8, Problem 21E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 13-24, find the indicated derivative.Find y ( 4 )  if  y ' = 4 x − 1

To determine

To calculate: The value of y(4) if the first derivative for the function is y=4x1.

Explanation

Given Information:

The first derivative for the function is y=4x1.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

According to the chain rule of derivatives, if there is a function of form y=f(u(x)), then its derivative is,

dydx=f(u(x))u(x)

Calculation:

Consider the provided first derivative for the function,

y=4x1=(4x1)12

Differentiate both sides with respect to x,

y(2)=ddx((4x1)12)

Apply the chain rule of derivatives,

y(2)=12(4x1)121(ddx(4x1))=12(4x1)12(ddx(4x)ddx(1))=12(4x1)12(4x110)=2(4x1)12

To find the value of y(3), differentiate both sides of y(2) with respect to x,

y(3)=ddx(2(4x1)12)=2d

### 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

#### Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### The normal plane to at t = 1 has equation:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Define the concept of internal validity and a threat to internal validity.

Research Methods for the Behavioral Sciences (MindTap Course List)

#### Explain the distinction between science and pseudoscience.

Research Methods for the Behavioral Sciences (MindTap Course List) 