Find frac{dy}{dx}, if y+sin y=cos x. | vedclass

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(A) We differentiate the given equation $y+\sin y=\cos x$ with respect to $x$:$\frac{d}{dx}(y) + \frac{d}{dx}(\sin y) = \frac{d}{dx}(\cos x)$Using the

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$-\frac{\sin x}{1+\cos y}$

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(A) We differentiate the given equation $y+\sin y=\cos x$ with respect to $x$:$\frac{d}{dx}(y) + \frac{d}{dx}(\sin y) = \frac{d}{dx}(\cos x)$Using the chain rule for $\frac{d}{dx}(\sin y)$:$\frac{dy}{dx} + \cos y \cdot \frac{dy}{dx} = -\sin x$Factor out $\frac{dy}{dx}$:$\frac{dy}{dx}(1 + \cos y) = -\sin x$Therefore,the derivative is:$\frac{dy}{dx} = -\frac{\sin x}{1+\cos y}$where $y 
eq (2n+1)\pi$.

Find $\frac{dy}{dx},$ if $y+\sin y=\cos x$.

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