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Find an equation of the tangent line to the given curve at the specified point.
$ y = \frac {x^2 - 1}{x^2 + x + 1}, (1,0) $
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01:14
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Oregon State University
Harvey Mudd College
University of Nottingham
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.
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06:43
Hey, it's from someone. You rain here, so we have. Why is equal to X square minus one all over X square plus X plus one. We're gonna use the quotient role to find the derivative when we get X square minus one The derivative X square plus X plus one minus X square minus one and the derivative of X square plus X plus one This is all over X square plus X plus one square. When we simplify this, we get X square. It was for X plus one while over at square, less X plus one square. So to find a slope of the tangent line at one comma zero we're gonna plug in X is equal to one into our derivative when we get 2/3. So we're gonna create a line Why is equal to 2/3 X minus one plus zero? This becomes equal to two birds. X minus 2/3
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