If \(y + \sin y = \cos x\), where \(1 + \cos y \ne 0\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(-\displaystyle\frac{\sin x}{1 + \cos y}\)
By implicit differentiation with respect to x (y is a function of x):
\( \displaystyle \frac{dy}{dx} + \cos y\,\frac{dy}{dx} = -\sin x \)
\( \displaystyle (1 + \cos y)\frac{dy}{dx} = -\sin x \)
\( \displaystyle \frac{dy}{dx} = -\frac{\sin x}{1 + \cos y} \)