Answer
$dy/dx=\frac{-ysin(xy)}{cosy+xsin(xy)}$
Work Step by Step
Take the derivative as is on either side of the equation:
$-sin(xy)\times(x(dy/dx)+y)=0+(dy/dx)cos(y)$
Move all terms with dy/dx onto one side of the equal sign and distribute the dy/dx out of each term:
$(dy/dx)\times(cosy+xsin(xy))=-ysin(xy)$
Isolate dy/dx by dividing both sides by the terms:
$dy/dx=\frac{-ysin(xy)}{cosy+xsin(xy)}$
