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

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00:29

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Campbell University

Oregon State University

Baylor University

Idaho State University

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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05:35

Here's our function. G up data equals co sign square data. And remember, when you see co sign square data, what it means is that you take in co sign data and squared it. So this is a composite function. We have one function inside another, and so we're going to differentiate it using the chain rule. And so that means we need to find the derivative of the outside function and multiply it by the derivative of the inside function. So are derivative will call g prime of data, and the outside function is the squaring function. And it's derivative would be if we bring down the two and then we raised the inside to the one to the first because we subtract one to get the new power. Now we multiply by the derivative of the inside and the inside is co sign data and the derivative of co sign is negative sign. So we have negative sign data, so we have our derivative and now we're just going to simplify so we can bring the negative and the two together and we have negative to co sign data signed data

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