I assume you are studying implicit differentiation. Solving for dy/dx.
For the Left side use product rule. For Right side, use chain rule. Remember any time you take derivative of "y-term" you must multiply it by dy/dx.
---> [tex]\frac{dy}{dx} e^y cos (x) - e^y sin(x) = (y + x \frac{dy}{dx}) cos (xy)[/tex]
Get dy/dx terms on one side:
[tex]\frac{dy}{dx} e^y cos (x) - \frac{dy}{dx} x cos(xy) = e^y sin(x) + y cos (xy)[/tex]
Factor out dy/dx and solve:
[tex]\frac{dy}{dx} (e^y cos (x) - x cos(xy)) = e^y sin(x) + y cos (xy) \\.......\\ \frac{dy}{dx} = \frac{e^y sin(x) + y cos (xy) }{e^y cos (x) - x cos(xy)}[/tex]
