Problem

Find the derivatives of the given functions. $$y=…

Problem 26 Easy Difficulty

Find the derivatives of the given functions.
$$y=\sqrt{\sin ^{-1}(x-1)}$$

Answer

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

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

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Video Transcript

All right. We want to find it rid of dx for the function. Why is equal to the square root Of Arc Sine X -1. To solve the great need to rely on the table to shortcuts. We picked up through a single variable calculus, particularly, we need to use our recently learned university econometric evidence. So I've listed here the three major investment. Your evidence for this problem. We need to use that DDX Arson X is 1/1 minus X squared. You also, we're going to have to make use of the general since our arc sine function is square root. So we can rewrite Why? Ask arc sine X minus one race and power of one half, which makes recognizing how to use the chain will hear a bit easier that we proceed to the derivative. So by the chain rule we have D D X equals one half. Arc sine x minus one of the negative one half. Or root arc sine x minus one times 1/1 minus x minus one squared, thus simplifying the denominator in the right hand turn and putting our arc sine x minus one reason everyone happens to nominated as well. We have solution dy dx equals one over to root arc sine x minus one times two x minus x squared.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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