Question

How do you differentiate `sin (xy) = x^2 - y^2`?

Answer 1

In deriving remember that `y` is a fnction of `x`:
`cos(xy)*(y+xdy/dx)=2x-2y(dy)/dx`
`ycos(xy)+x(dy)/dxcos(xy)-2x+2y(dy)/dx=0`
`(dy)/dx[xcos(xy)+2y]=2x-ycos(xy)`
And finally:
`(dy)/dx=(2x-ycos(xy))/(xcos(xy)+2y)`