Answer
$dy/dx=\frac{-siny-ycosx}{sinx+xcosy}$
Work Step by Step
Take the derivative as is on either side of the equation:
$xcosy\times(dy/dx)+siny+ycosx+sinx\times(dy/dx)=0$
Isolate all terms with dy/dx onto one side of the equal sign and distribute the dy/dx out of each term:
$dy/dx(sinx+xcosy)=-siny-ycosx$
Isolate dy/dx by dividing both sides by the terms:
$dy/dx=\frac{-siny-ycosx}{sinx+xcosy}$
