54. y xe, (0, 0) -x2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 31E
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please find the equation of the tangent line to the curve at the given point (provided in the images)

54. y xe, (0, 0)
-x2
Transcribed Image Text:54. y xe, (0, 0) -x2
Expert Solution
Step 1

Given,

y xe
Now, Finding the derivative of y, we get
dy d(xe*)
dx
dx
Using product rule, we get
d(x)
d(e*)
x
dx
-x
dx
e-x x 1 xe-*(-1)
= e*(1 - x
dy
Slope at the point (0,0) is
e-(1 -0) 1
dx
So, equation of the tangent at the point (0,0) is
у — 0 %3D 1(х — 0)
у 3D х
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