Implicit differentiation and inverse trigonometric functions practice question 10

$y$ appears on both sides of the equation, once inside a sine. When you differentiate with respect to $x$, what does every term built from $y$ pick up?

Differentiating $\sin(y)$ with respect to $x$ gives $\cos(y)\dfrac{dy}{dx}$, not $\cos(y)$.

Gather both $\dfrac{dy}{dx}$ terms on one side and factor.