sin x + 2 cos 2y = 1
cos x - 4(sin 2y)dy/dx = 0
dy/dx = cos x/4 sin 2y

I understand how to get from step 2 to step 3, and I understand part of step two (cos x is the derivative of sin x, so that makes sense, and the negative part of the next part comes from the fact that the derivative of cos x is -sin x), but how exactly does the 4(sin 2y) come about?

sin x + 2 cos 2y = 1
cos x - 4(sin 2y)dy/dx = 0
dy/dx = cos x/4 sin 2y

I understand how to get from step 2 to step 3, and I understand part of step two (cos x is the derivative of sin x, so that makes sense, and the negative part of the next part comes from the fact that the derivative of cos x is -sin x), but how exactly does the 4(sin 2y) come about?