Here you must make use of product rule on the right side and implicit differentiation.
x * sec²(y) * y' + tan(y) = y'
Then just rearragnge to solve for y'
x * sec²(y) * y' - y' = -tan(y)
y'(xsec²(y) - 1) = -tan(y)
y' = -tan(y) / [xsec(y) - 1]
y = 1/sin(x-sinx)
Here, all that you have to keep in mind is that the derivative of sec(u) = sec(u)tan(u) * du/dx
The du/dx is not officially a part of the derivative of sec(x), it is just there to remind you of chain rule. (where u = x - sin(x))