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Find the derivative of the function. Simplify where possible.$ g(x) = \arccos \sqrt x $

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00:32

Frank Lin

00:50

Doruk Isik

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

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.

01:43

Find the derivative of the…

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01:16

Use the Product Rule to fi…

01:57

Find the first derivative.…

this problem. We're gonna be working on the derivatives of inverse trig functions. Um, and in this case, we're going to be discussing the inverse of CoSine. So our function is g of X is equal to the inverse cosine or the arc co sign of the square root of X. So this is our function, and then we want to take its derivative. So remember that the derivative of an R CoSine or the derivative of the universe coastline is negative one over the square root of one minus X squared. But keep in mind that the ex portion is whatever is inside the parentheses, so what we'll end up getting as a result. Since this is square root, we'll just get X because we'll have a square root of X squared, subtle. Cancel out then what we have is a result is we need to make sure that we multiply this using chain role. We multiply this kind of the derivative, so that's going to be one over to root X. That's the derivative of what's inside the parentheses. So our final answer, what we'll see is we'll end up getting a negative 1/2 times the square root of X minus X squared. And that's just through distributing this with the other portion of the square root. So this will be our final answer, and this is what we have for white crime.

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