You need to differentiate both sides with respect to x such that:

`2x + 2y*(dy)/(dx) = cos(xy)*(y + x*(dy)/(dx))`

You need to find `(dy)/(dx), ` hence, you need to isolate the terms that contains `(dy)/(dx)` to the left side such that:

`2y*(dy)/(dx) - x*cos(xy)*(dy)/(dx) = y*cos(xy) - 2x`

Factoring out `(dy)/(dx)` yields:

`(dy)/(dx) (2y - x*cos(xy)) = y*cos(xy) - 2x`

`(dy)/(dx) = (y*cos(xy) - 2x)/(2y - x*cos(xy))`

**Hence, evaluating `(dy)/(dx)` yields `(dy)/(dx) = (y*cos(xy) - 2x)/(2y - x*cos(xy)).` **

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