   Chapter 3.1, Problem 35E ### 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 an equation of the tangent line to the curve at the given point. y = x + 2 x , ( 2 , 3 )

To determine

To find: The equation of the tangent line to the curve at the point.

Explanation

Given:

The curve y=x+2x.

The point is (2,3).

Derivative rules:

(1) Constant Multiple Rule: ddx[cf(x)]=cddxf(x)

(2) Power Rule: ddx(xn)=nxn1

(3) Sum Rule: ddx[f(x)+g(x)]=ddx(f(x))+ddx(g(x))

Formula used:

The equation of the tangent line at (x1,y1) is, yy1=m(xx1) (1)

where, m is the slope of the tangent line at (x1,y1) and m=dydx|x=x1.

Calculation:

The derivative of y is dydx, which is obtained as follows.

dydx=ddx(y) =ddx(x+2x)

Apply sum rule (3) and constant multiple rule (1),

dydx=ddx(x)+ddx(2x)=ddx(x)+ddx(2x1)=ddx(x)+2

### 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 37-44, perform the indicated operations and simplify. 42.

Mathematical Applications for the Management, Life, and Social Sciences

#### Give the formula for the inverse of the 22 matrix. A=[abcd].

Finite Mathematics for the Managerial, Life, and Social Sciences

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: If f(x) = f (−x) for all x then .

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

#### What is the goal of a single-case experimental research design?

Research Methods for the Behavioral Sciences (MindTap Course List) 