Derivatives of trigonometric functions: Find the derivative dy/dx for cos [sec (xy)] = cos x sec y?

I've tried implicit differentiation, ie.
d/dx [cos (sec (xy))] = d/dx (cos x sec y)

For right-hand-side,
d/dx (cos x sec y)
= [(d/dx cos x) (sec y)] + [(cos x) (dy/dx d/dy sec y)]
= [(-sin x) (sec y)] + [(cos x) (sec y) (tan y) (dy/dx)]

For left-hand-side,
d/dx [cos (sec (xy))]
"and I have no idea to go on..."

Please help, thanks a lot!