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Numerade Educator

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Problem 52 Easy Difficulty

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

Answer

$-\frac{1}{2} \frac{1}{\sqrt{x-x^{2}}}$

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Video Transcript

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.