Question

For \[y+\sin y=\cos x\], which equation results after differentiating both sides with respect to \[x\] and using the chain rule?

Options

• \[\frac{dy}{dx}+\sin y\cdot\frac{dy}{dx}=\cos x\]

• \[\frac{dy}{dx}+\cos y=-\sin x\]

• \[y+\cos y=-\sin x\]

• \[\frac{dy}{dx}+\cos y\cdot\frac{dy}{dx}=-\sin x\]

Answer 1

The derivative of \[y\] is \[\frac{dy}{dx}\]. Also, \[\frac{d}{dx}(\sin y)=\cos y\cdot\frac{dy}{dx}\], while \[\frac{d}{dx}(\cos x)=-\sin x\].