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Differentiate.

$ y = \frac {1}{t^3 + 2t^2 - 1} $

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$\frac{d y}{d t}=\frac{-t(3 t+4)}{\left[t^{3}+2 t^{2}-1\right]^{2}}$

00:36

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Oregon State University

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.

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he? It's Claire's. So when you're in here so I'm gonna take the derivative in terms of tea or one over T cute plus two teeth square plus minus one When we get negative. D over D t. Is he cute? Plus two T square minus one over T cute plus two key square minus one square When we get negative. Three T Square plus two times two T plus Cyril all over T cute plus two teeth square minus one square. We're getting negative. T times three T plus four over t cubed close to T square minus one square.

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