Download the App!

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

Question

Answered step-by-step

Find the derivative of the function. Simplify where possible.$ y = \cos^{-1} (\sin^{-1} t) $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Carson Merrill

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

00:55

Frank Lin

Doruk Isik

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Faith A.

October 1, 2020

Campbell University

Baylor University

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.

01:21

Find the derivative of the…

01:08

01:03

02:56

Find the derivative.$$…

02:24

00:44

03:17

01:04

01:37

02:14

00:31

So if this problem we're gonna be utilizing the derivative of inverse trig functions on this will be useful because we use inverse trig functions in math, they come up. So if we want to find the rate of change or the the slope of a tangent line of the graph, then we're gonna want to utilize in verse trig function identities on derivatives. So keep in mind that what we have in this case is the inverse coastline. So why equals the inverse coastline of the inverse sign of key? It could be acts, but in this case, it's teeth. All right, that's what we have. Remember that the derivative of the inverse coastline is one is negative. One over the square root of one minus X squared, where X is what's inside the parentheses. So now it will end up getting. Is that why crime is equal to negative one over the square root of one minus sine inverse of tea square? Yeah, And then, since we have to do change rule here, we're gonna multiplying that by the derivative of what's inside the parentheses, which that's another trick function in verse, trick function. That will be one over the square root of one minus. He squared because that's what happens when you take the derivative of the inverse sign of tea. Then we can multiply all this together to simplify it further. What will end up getting as a result is why prime being equal Thio negative one over the square root of one. Basically everything we see here. Uh, the only difference is we can just copy and paste this thing. Only difference is now we can multiply this bottom portion, uh, at the bottom. So we'll have times That's right here. And that will be our final answer for the derivative of why?

View More Answers From This Book

Find Another Textbook

04:23

A particle is moving along the curve whose equation is (xy^3)/(1+y^2)= 8/5. …

01:27

use 3.14. How much foil is required to cover a rectangular box that is 4in b…

02:07

How do you factor this completely:x^3 + ax + 3a + 3x^2

A surveyor sights the far bank of a river at an angle of 110˚ to the near ba…

00:33

how can i convert radians to degrees?

03:52

A train travels from city A to city B and then to city C. The distance from …

04:28

Completing the Square1) 9m^2 - 20m - 21 = 02) 10x^2 - 4x -32 = 0

02:35

The measure of a single angle in a regular octagon is (4x + 12)°. Find the v…

01:30

write an equivalent expression as 18 the denominator 5/9

04:30

A man is 6ft tall is standing 10 feet from the base of a lamp post. The mans…