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Find the derivatives of the given functions.$$y=\sin ^{-1} x-\sqrt{1-x^{2}}$$

$\frac{d y}{d x}=\frac{1+x}{\sqrt{1-x^{2}}}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

Derivatives

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uh huh. We want to find the derivative dy dx for the function. Why is equal to the arc sine of x minus the square root of one minus x square. To solve this problem, we need to rely on differentiation shortcuts. We picked up through a single variable calculus in addition to the inverse trig derivatives, we recently learned. So we have the three major industry directors listed here for this problem. We need to use the fact that DDS arc sine X equals 1/1 minus x square. We also need to use the chain rule for the term route one minus X square. Specifically, we can rewrite what I asked. Arc sine X minus one minus X squared because also right route one minus X squared as one minus X squared, which is the power of one half. So we can proceed now to take the derivative dust. Dy dx is 1/1 minus X squared. This is the river of arc sine X minus negative two X over to root, woman is X squared. This is the derivative of route one minus X squared, taking the chain rule. Thus combining our denominators, we have solution DY dx equals two minus two X over to route one minus X squared.

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