   Chapter 3.1, Problem 34E ### 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 = 2ex + x, (0, 2)

To determine

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

Explanation

Given:

The curve is, y=2ex+x.

The point is (0,2).

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))

(4) Derivative of natural exponential function: ddx(ex)=ex

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(2ex+x)

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

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

Apply rule (4) and the power rule (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 Exercises 13-20, sketch a set of coordinate axes and plot each point. 18. (52,32)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### CHECK POINT Given the sets and, find the following. 8.

Mathematical Applications for the Management, Life, and Social Sciences

#### Find the eleventh term of the arithmetic progression a+b,2a,3ab,

Finite Mathematics for the Managerial, Life, and Social Sciences 