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Find the derivative of the function.$ J(\theta) = \tan^2 (n \theta) $

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00:42

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Michaels M.

October 25, 2021

Use logarithmic differentiation to find the derivative of the function. y = x2 cos(x)

Missouri State University

Campbell University

Harvey Mudd College

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.

00:55

Find the derivative of the…

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How to solve?

all right. So here we have J of data and it's a composite function. We have a function inside of function. Actually, we have three layers function inside a function inside function. So we're going to use the chain rule to find the derivative. I remember when you see Tangent Square data, what it means actually is you're taking the tangent in this case of in data and that whole thing is being squared the square it is actually on the very outside. That's our outermost function. So now, to find the derivative, what we want to do is use the chain rule, first of all, the derivative of the squaring function, bring down the two and then raised tangent of Anthea to the first. And then we multiply by the derivative of the tangent and derivative of tangent is he can't squared. So we multiply by c can't squared of Anthea and then we multiply by the derivative of the very inside part the derivative of in data is in. So if we write that in a simplified way, by just multiplying the two and the end together we have to end times the tangent of and data times a C can't squared of in data

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