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Find the derivative of the function.$ f(\theta) = \cos (\theta^2) $

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$=-2 \theta \sin \left(\theta^{2}\right)$

00:12

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Missouri State University

Campbell University

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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Find the derivative of the…

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Find the derivative.$f…

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01:38

Differentiate.

$ …

here's our function, and it's a composite function because it has one function inside the other. And so we're going to find the derivative using the chain rule and so f prime of data. The derivative would be the derivative of the outside function times, the derivative of the inside function, and the outside function is co sign, and it's derivative is negative sign. So we have negative sign of data squared. Whatever was in there still in there times the derivative of the inside and the inside is they two squared, so it's derivative would be to fade up. Okay, so we have our derivative and now we just want to simplify it so we could multiply the tooth data and the negative one. And we have negative two theta sign of state a squared

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