I am asked to find the points on the curve at white the tangent is horizontal, for the function:
$$y=\frac{\cos x}{2+\sin x}$$
To find the points at which the tangent is horizontal, I need to know what values will result in the derivative of the function equaling zero, so I differentiate using quotient rule:
$$y'=\frac{(-2\sin x-\sin^2 x)-\cos^2 x}{(2+\sin x)^2}$$
The algebra in simplifying the derivative from here is what is holding be back. Also, have I differentiated this correctly?