I understand how to find the stability of fixed points by using $f'(x)$ and inserting the values of the fixed points into that. However, I can't figure out how to tell the stability in systems such as
$$\frac{dx}{dt} = a + \sin(x) + \cos(2x)$$
In situations like this, the value of the fixed points varies as '$a$' changes, which I have no trouble finding, its just defining their stability that I struggle with.