x^2-4xy-5y^2=1999

x^2-4xy-5y^2=1999

d/dx (x^2) - d/dx (4xy) - d/dx (5y^2) = d/dx (1999)

2x (d/dx (4x) y+4x*d/dx (y)) - d/dy (5y^2) * dy/dx=0

2x - (4y+4x*d/dy (y) * dy/dx) - 5*d/dy (y^2) * dy/dx=0

2x - (4y+4x*1*dy/dx) - 5*2y*dy/dx=0

2x - (4y+4x*dy/dx) - 10y*dy/dx=0

2x-4y-4x*dy/dx-10y*dy/dx=0

-4x*dy/dx-10y*dy/dx=-2x+4y

(-4x-10y) * dy/dx=-2x+4y

dy/dx=-2x+4y/-4x-10y

dy/dx=x-2y/2x+5y

dy/dx=x-2y/2x+5y