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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) $

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00:57

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

University of Nottingham

Idaho State University

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

02:35

Find equations of the tan…

01:47

Find equations of the tang…

01:52

Find an equation of the ta…

02:42

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

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