   Chapter 2.5, Problem 5E

Chapter
Section
Textbook Problem
1 views

# Write the composite function in the form f ( g ( x ) ) . [Identify the inner function u = g ( x ) and the outer function y = f ( u ) .] Then find the derivative d y / d x . y = sin x

To determine

To write:

The composite function in the form of f(g(x)) and find dy/dx

Explanation

Formula:

i. d(x)dx=12x

ii. ddxsinx=cosx

Rules:

a) Chain rule: If Fx=fogx=fgx then F'x=f'gx*g'(x)

Given:

y= sinx

Calculation:

Express y=fogx=f(gx) where y=fu=u  and u=gx=sinx

Since

f'(u)=dfdu=d(u)du

By using the formula

=12u

### 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

#### Determine the infinite limit. limx3x(x3)5

Single Variable Calculus: Early Transcendentals, Volume I

#### Find the derivative of the function. y=(x+1x)5

Single Variable Calculus: Early Transcendentals

#### True or False: converges.

Study Guide for Stewart's Multivariable Calculus, 8th

#### By definition the improper integral It is not an improper integral.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### If tan=1160, find sec and cot.

Elementary Geometry for College Students

#### Explain how inter-rater reliability is established.

Research Methods for the Behavioral Sciences (MindTap Course List) 