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Find equations of the tangent lines to the curve

$ y = \frac {x - 1}{x + 1} $

that are parallel to the line $ x - 2y = 2. $

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$y=\frac{1}{2} x+\frac{7}{2}, \quad y=\frac{1}{2} x-\frac{1}{2}$

01:28

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Campbell University

Harvey Mudd College

Idaho State University

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.

03:57

Find equations of the tang…

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$\begin{array}{c}{\text { …

07:11

Find equations of both lin…

03:31

Find an equation of the li…

01:11

09:52

02:20

Hey, it's clear. So when you re here so you have X minus two. Why is equal to two and this continue Y is equal to 1/2 X minus one. This is the M, which is the slope of the line. So here we're gonna find the derivative of the curve. Why is equal to X alertness one over X plus one. The derivative is equal to one times next, plus one minus one term X minus one over X plus worn square which becomes equal to two over X plus one square. So this is the slope of the tension line to Wyatt X. So when we plug in, make this equal to one. Have we get when half is equal to two over X plus one square that's can be equal to negative three or one. So we're gonna get the Y coordinates. So when X is equal to negative three Well, why is equal to two when X is equal to one? Why is equal to zero? We're gonna pluck the points and slope into the point slope line equation. So for a negative three korma too, we get why is equal to 1/2 x minus and negative. Three less, too, which is equal to one. Have X less stubborn has for one comma zero we have. Why is equal to one, huh X minus one plus zero, which is equal to 1/2 X minus one her.

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