   Chapter 3.5, Problem 57E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the derivative of the function. Simplify where possible.57. y = x sin − 1 x + 1 − x 2

To determine

To find: The derivative of the function.

Explanation

Given:

The function is y=xsin1x+1x2.

Derivative rules:

(1) Chain rule: dydx=dydududx

(2) Derivative of the inverse trigonometric function: ddx(sin1(x))=11x2.

Calculation:

Obtain the derivative of the function.

Consider the function y=xsin1x+1x2

Differentiate the function implicitly with respect to t,

dydx=ddx(xsin1x+1x2)=ddx(xsin1x)+ddx(1x2)

Apply the product rule (3) and simplify the expression,

dydx=xddx(sin1x)+sin1xddx(x)+ddx(1x2)=x[11x2]+sin1x(1)+ddx(1x2) [derivative rule (2)]

Let u=1x2

### 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

#### In Problems 15-20, find the indicated derivative. 19. Find

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the integral. 5. te3tdt

Single Variable Calculus: Early Transcendentals

#### In Exercises 110, find the graphical solution to each inequality. y3

Finite Mathematics for the Managerial, Life, and Social Sciences

#### Using the power series for cos x, the sum of the series is: cos(0.0625) cos(0.25) cos(0.5)

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

#### True or False: converges.

Study Guide for Stewart's Multivariable Calculus, 8th 