Answer
$dy/dx=\frac{-sin(x+y)-ycos(xy)}{xcos(xy)+sin(x+y)}$
Work Step by Step
Take the derivative as is on either side of the equation:
$cos(xy)\times(x(dy/dx)+y)=-sin(x+y)\times(1+dy/dx)$
Move all terms with dy/dx onto one side of the equal sign and distribute the dy/dx out of each term:
$dy/dx(xcos(xy)+sin(x+y))=-sin(x+y)-ycos(xy)$
Isolate dy/dx by dividing both sides by the terms:
$dy/dx=\frac{-sin(x+y)-ycos(xy)}{xcos(xy)+sin(x+y)}$
