Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the derivative of the following functions.$$y=\sin x \cos x$$

$cos^{2}x-sin^{2}x=$ cos $2x$

Calculus 1 / AB

Chapter 3

Derivatives

Section 5

Derivatives of Trigonometric Functions

Differentiation

Missouri State University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:43

Find the derivative of the…

02:47

00:45

01:19

07:42

02:38

04:53

04:20

03:57

06:05

So for this problem, were asked to find the derivative of sign of X Times Co sign of X. And because this is two functions being multiplied together, we have to use the product rule, which can be summarized on the right and bread. So we'll begin by defining our A and B terms so we can define a as a sign of X and therefore a prime being co sign of X and B. We can define as co sign of X with be prime being minus sign of X. So with that information we can define why prime being co sign of X Times Co sign of X plus sign of X times negative sign of X And when you simplify these terms, you get coastline squared of X minus sine squared of X, and this right here is a double angle identity. So be sure when you're solving derivatives to have those list of Trigon Amit identities on the side and this simplifies now to co sign of two x

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find the derivative of the following functions.$$y=x \cos x \sin x$$

Find the derivative of the following functions.$$y=x-\cos x \sin x$$

Find the derivative of the following functions.$$y=\sin x+\cos x$$

Find the derivative of the following functions.$$y=x \sin x$$

Find the derivative of the following functions.$$y=\frac{x \sin x}{1+\co…

Find the derivative of the following functions.$$y=\frac{\sin x}{1+\cos …

Find the derivative of the following functions.$$y=\frac{\sin x+\cos x}{…

Find the derivative of the following functions.$$y=\frac{\cos x}{\sin x+…

Find the derivative of the following functions.$$y=e^{x}(\cos x+\sin x)$…

Find the derivative of the following functions.$$y=\frac{1-\sin x}{1+\si…

10:16

Average and marginal profit Let $C(x)$ represent the cost of producing x ite…

02:21

Show two ways to differentiate $f(x)=\frac{1}{x^{10}}.$

05:56

Let $p(t)$ represent the population of the Las Vegas metropolitan area $t$ y…

01:06

Derivatives Find the derivative of the following functions. See Example 2 of…

04:34

Limit proofs Use the precise definition of a limit to prove the following li…

01:13

Evaluate limit.$$\lim _{t \rightarrow 2} \frac{t^{2}+5}{1+\sqrt{t^{2}+5}…

03:18

Slant (oblique) asymptotes Complete the following steps for the given functi…

02:42

Sketching derivatives Reproduce the graph of $f$ and then plot a graph of $f…

Derivativesa. Use limits to find the derivative function $f^{\prime}$ fo…

01:45

Determining the unknown constant Let$$ f(x)=\left\{\begin{array}{ll} 2 x…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.