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Solve the given problems.Find the derivative $\frac{d y}{d x}$ of the implicit function $x \cos 2 y+\sin x \cos y=1$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

06:08

Use implicit differentiati…

04:11

Find $d y / d x$ by implic…

03:59

03:21

Find $ y" $ by implic…

02:45

04:09

05:06

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03:03

we want to find Dy dx for the function X. Coast two Y plus sign X. Cosign Y equals one to do so we rely on differentiation shortcuts we picked up through a single variable calculus, particularly Rule +03 listed here on Electoral zero is D V. X. In Mexico's Cossacks. GDX Coast Mexico's native syntax rules one through three. Other power rule product rule in chain rule respectively. Were also going to be relying on rule three in the sense that because both sides of this equation include Y. Or rather this is not simply a function of why we're gonna have to reform implicit differentiation. So we have an implicit differentiation DDX exposed to Y plus sign. Mexico's Y equals C. D. X. One. The right hand side of course just become zero and are conservative becomes coast to y minus two. X. And Y. Dy dx This from product in the first term plus coast, ex coast Y minus sine X. And Y. Dy dx. Product in the second term equal zero. Thus solving for DY DX gives you I. D. X equals Coast two Y plus Coast. Excuse why over two X into Y, person, X and Y.

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