Problem

(a) The curve $ y' = 1/(1 + x^2) $ is called a wi…

02:32

Problem 34 Medium Difficulty

Find equations of the tangent line and normal line to the given curve at the specified point.

$ y = \frac {2x}{x^2 + 1}, (1,1) $

Answer

Tangent line is $y=1$
Normal line is $x=1$

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00:57

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

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Video Transcript

he It's clear. So when you right here, So we have of X is equal to two x over X square plus one. We're gonna difference she using the product quotient rule to get X square plus one D over DX for two x minus two X d over D X for X square plus one all over X square plus one square. This becomes equal to X square plus one times two minus two X tones to X all over X square plus one square, which is equal to two minus two X square over X square plus one square. A slip of detention at one common one become zero, and the equation of change in is why minus one over X minus or unequal. Ciro. So why is equal to one? And we know that the normal line is perpendicular, so it's going to be access equal to one

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Top Calculus 1 / AB Educators

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Michael J.

Idaho State University

Joseph L.

Boston College