Question

find DY/DX if Y + sin y = cos x​

Answer 1

HERE IS YOUR ANSWER

Y+siny = cosX

differentiate with respect to X:-

Dy/DX + cosy × Dy/DX = -sinx

Dy/DX = -sinx / ( 1+cosX) ANS.

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Answer 2

$\bf \large Solution$

●we we differentiate the relationship directly with respect to X.

$\bf \large\frac{dy}{dx} + \frac{d}{dx}( sin \: y) = \frac{d}{dx} ( cos \: x) \\ \\ \bf \large \: which \: implies \: using \: chain \: rule \\ \bf \frac{dy}{dx} + \cos(y) . \frac{dy}{dx} = - \sin(x) \\ \bf this \: gives \: \frac{dy}{dx} = - \frac{ \sin(x) }{1 + \cos(y) } \\ \bf y \: is \: not \: equal \: to \: (2n + 1)\pi$

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