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 derivatives of the given functions.$$y=3\left(4-\cos ^{-1} 2 x\right)^{3}$$

$\frac{d y}{d x}=\frac{12\left(4-\cos ^{-1} 2 x\right)^{2}}{\sqrt{1-4 x^{2}}}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

Derivatives

Missouri State University

Campbell University

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

04:26

Find the derivatives of th…

00:35

02:32

Find the derivative of the…

00:42

02:55

Calculate the derivative o…

00:41

00:51

04:50

00:37

Find derivatives of the fu…

01:33

Okay, we want to find the derivative Dy dx for the expression. Three times four minutes are chosen to execute to solve. We're going to use differentiation shortcuts. We picked up threats and variable calculus in particular, we're going to use the inverse trig derivatives that we've recently learned. So we have three major inverse trig derivatives listed here. We're going to primarily used for this problem. DDX Arcos X equals negative 1/1 minus square will also use the chain rule since four months are chosen to execute. Since why is already written in its most easily differential form, we can proceed now to solve so we have by the chain rule, Dy dx equals three times three times four minutes are closing two X squared times the derivative of what's inside our parentheses, which is derivative. Four minutes arcos into X or two over route one minutes four X square for this we should be taking the negative but since negative are cruisin two X has a negative in front, the negatives cancel. Thus, we have final solution. DY Dx equals 18 times four minus our cousin two X squared all over Route one minus four X squared.

View More Answers From This Book

Find Another Textbook

Numerade Educator

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 derivatives of the functions.$$y=(4 x+3)^{4}(x+1)^{-3}$$

Find the derivatives of the functions defined as follows.$$y=\cos \left(…

Find the derivative of the function.$y=a^{3}+\cos ^{3} x$

Find the derivative of the function.$y=\cos \left(a^{3}+x^{3}\right)$

Calculate the derivative of the following functions.$$y=\cos ^{7 / 4}\le…

Find the derivatives of the functions defined as follows.$$y=-3 e^{2 \si…

Find the derivatives of the following functions.$$f(x)=3 x^{3}-\frac{4}{…

Find derivatives of the functions defined as follows.$$y=3 \cdot 4^{x^{2…

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.