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Differentiate.
$ y = \frac {t^3 + 3t}{t^2 - 4t + 3} $
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00:37
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
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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It's clear, so inhumane here. So we're gonna differentiate this in terms of tea. We got t cute plus three tea over T Square minus 40 plus three just becomes equal to D over DT T Q plus three p comes T Square minus 40 plus three minus three Q plus three T terms de over de ti oh, teeth square minus 40 plus three. All over he square minus 40 plus three squared. Can we get three T Square plus three times one comes T square minus 40 plus three minus two tea minus or times one plus Cyril Terms T Acute plus three t all over T square minus 40 plus three square. This becomes equal to T square T to the fourth minus a T cubed plus 60 square less nine over P square minus 40 plus three where
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