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If $ H(\theta) = \theta $ sin $ \theta, $ find $ H'(\theta) $ and $ H"(\theta). $

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00:54

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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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01:37

$$\text { Let } \mathcal{A…

0:00

Differentiate.$h(\thet…

we're so when you married here. So we her Rita which is equal to data sign Fada. So what's take the first derivative? And we use the product rules. We get the derivative of data I'm sign, plus data times the derivative of sign. And this gives us signed data Rita Co sign Next. We're going to take the second derivative using the first derivative so they get co sign, plus the derivative of data we'll sign, plus data turns the derivative of co sign. And this gives us one negative sign, which gives us two SCO sign minus data sign.

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