   Chapter 3.2, Problem 32E ### 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 given curve at the specified point. y = 1 + x 1 + e x ,   ( 0 , 1 2 )

To determine

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

Explanation

Given:

The curve is y=1+x1+ex.

The point is (0,12).

Derivative rules:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2x]2

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

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

(4) Natural exponential function: ddx(cf)=cddx(f)

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(1+x1+ex)

Apply the quotient rule (1) and simplify the terms,

dydx=(1+ex)ddt(1+x)(1+x)ddx(1+ex)(1+ex)2

Apply the derivative rule (3),(4) and (2),

dy</

### 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 