Question

Find \[\frac{dy}{dx}\] if \[y+\sin y=\cos x\].

Options

• \[-\frac{\sin x}{1+\cos y}\]

• \[\frac{\sin x}{1+\cos y}\]

• \[-\frac{\cos x}{1+\sin y}\]

• \[-\sin x(1+\cos y)\]

Answer 1

Differentiation gives \[\frac{dy}{dx}+\cos y\cdot\frac{dy}{dx}=-\sin x\]. Factoring \[\frac{dy}{dx}\] gives \[(1+\cos y)\frac{dy}{dx}=-\sin x\], so the stated derivative follows.