Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Differentiate.

$ f(\theta) = \theta $ cos $ \theta $ sin $ \theta $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$f^{\prime}(\theta)=1 \cos \theta \sin \theta+\theta(-\sin \theta) \sin \theta+\theta \cos \theta(\cos \theta)=\cos \theta \sin \theta-\theta \sin ^{2} \theta+\theta \cos ^{2} \theta$ $=\sin \theta \cos \theta+\theta\left(\cos ^{2} \theta-\sin ^{2} \theta\right)=\frac{1}{2} \sin 2 \theta+\theta \cos 2 \theta$

01:18

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Campbell University

Oregon State 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.

01:38

$ …

02:10

01:26

Find the derivative.$f…

01:12

Differentiate.$f(\thet…

01:48

Compute the derivative. <…

02:25

00:33

Find the derivative of the…

01:46

Differentiate the function…

02:06

00:59

it's clear. So when you right here. So we're gonna take the derivative of data. Co. Sign time sign. This is gonna be equal to the over D Saito data Times co sign I'm signed. Let's stay tha d over. D aceto of co Sign time Signed list data D over defeat Ill of sign Times CO Something This becomes equal to co sign. I'm sign minus data signed. Square plus Data Co sign Square, which is equal to co sign I'm signed. WAAS Data Terms Co. Sign square minus sign square and we're using our double angle trick identities, which gives us one have sign to data plus data co sign to data.

View More Answers From This Book

Find Another Textbook

01:16

Question 12 ptsWhich of the following is not a measure of center?

01:59

Let Dx be the linear transformation from C'[a, b] into C[a, b] Find the…

03:49

Determine the formula of a quartic polynomial, p(z) , that has graph which i…

02:52

point) Evaluate the triple integralI zyav where E is the solid tetrahedo…

04:34

Using the trigonometric substitution, the integral(x2 49) Vxz 49is e…

04:49

Use the elimination method to find a general solution for the given linear s…

02:55

The graph of f' on the interval [ - 10, 5] is shown in the figure to th…

01:31

Use the graph of to find the largest open interval on which f is increasing_…

01:04

3 - National mixer, Inc , sells can openers. Monthly sales for a seven-month…