   Chapter 3.2, Problem 33E ### 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 equations of the tangent line and normal line to the given curve at the specified point.y = 2xex, (0, 0)

To determine

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

Explanation

Given:

The equation of the curve y=2xex.

The curve passing through the point (0,0).

Derivative rules:

(1) Product Rule: ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)]

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

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

(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)

The equation of normal line at (x1,y1) is, yy1=1m(xx1) (2)

Here, 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(2xex)

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

dydx=2xddx(ex)+exddx(2x)</

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