Find dy/dx by implicit differentiation 2sinxcosy=1

For the sake of simplicity, divide this equation thru by 2 to obtain

sinx cos y = 1/2.

Note that sinx cosy is a product, so apply the product rule:

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

Solve this for dy/dx:

(sin x)(sin y) (dy/dx) = cos x cos y

                          cos x cos y
Then dy/dx =  (answer)
                         sin x sin y