Partial derivatives sin(xcosy)

From the homework answers...

let "a" be a constant.

d/dx sin(x cos(a) = cos(a) cos(x cos(a)

d/dy sin(a cos(y) = -a sin(y) cos(a cos(y))

I don't understand how the above derivatives work, could someone explain how these are so or fill in a skipped step?

thanks in anticipation!!!

Holding y constant,
(∂/∂x) sin(x cos y) = cos(x cos y) * (∂/∂x) (x cos y) = cos y * cos(x cos y).

Similarly holding x constant,
(∂/∂y) sin(x cos y) = cos(x cos y) * (∂/∂y) (x cos y) = -x sin y * cos(x cos y).

I hope this helps!