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Find the derivatives of the given functions.$$y=6 \cos ^{-1} \sqrt{2-x}$$

$\frac{d y}{d x}=\frac{3}{\sqrt{x-1} \sqrt{2-x}}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

Derivatives

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

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we want to find dy dx the river Y. With respect to X. For the function. Why is equal to six? Our coastline of route two minus X. In this problem, we need to rely on the rate of shortcuts that we picked up through a single variable calculus in particular, we need to use our newly learned inverse trig and metric derivatives. So I have listed here the three major inverse trig derivatives. In particular. We need to use that. DDS arcos X equals negative one over square root one minus X squared. Since the argument of our coast is square root two minus X. Were also we need to make use of the chain rule, which we've learned before to solve this so we can rewrite why as six our coast to minus 61 half. That makes it easier to see how the chain will gets used in the argument. Our coast. Thus we have our derivative. Do I. D. X equals negative six over square root one minus two minus x square times by chain rule driven. What's inside parentheses? Or our coasts? One half, two minus X, negative one half times negative one. Thus are negatives cancel. We multiply our constants out and we shift our two minus X, the negative one half of the numerator denominator to obtain solution three over square root two minus X times x minus one.

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