Find d y d x , if y + sin y = cos x. - Vidyadip

Question

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

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Answer

We differentiate the relationship directly with respect to x, i.e.,
$\frac{d y}{d x}+\frac{d}{d x}$(sin y) = $\frac{d}{dx}$ (cos x)
which implies using the chain rule
$\frac{d y}{d x}+\cos y \cdot \frac{d y}{d x}$= - sin x
This gives $\frac{d y}{d x}=-\frac{\sin x}{1+\cos y}$
where $y \neq(2 n+1) \pi$

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