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(a) The curve $ y' = 1/(1 + x^2) $ is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point $ (-1, \frac {1}{2}).(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

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01:12

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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.

10:48

(a) The curve $ y' = …

04:30

$\begin{array}{l}{\text { …

03:26

The curve y = 1/(…

The curve y = 1/(1 + x^2) …

03:11

(a) The curve Y = 1/(1…

01:40

'(a) The curve Y = 1/…

02:14

(a) Find an equation of th…

02:37

02:58

(a) The curve $ y = \mid x…

02:59

(a) The curve $ y = x/(1 +…

03:42

it's clear. So a new ranger So we're given why is equal to one over one plus x square. So we need to find the derivative of this and we're gonna use the quotient role, which gives us one plus x square. Comes the derivative of one minus one times the derivative of one plus X square all over one plus x square square. And this gives us negative to X over one plus x square square. No, we plug in to find a slope and we get 1/2 when we substitute the equation for why minus 12. 1/2 is equal to em. Times X plus one we get Why minus one have this equal to 1/2 times X plus one. And this becomes why is equal to when have X plus one. And for part B, we're gonna draw our graph. You don't look like this in our tangent line in red

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