Hello,
[tex]f(x,y)=sin(xy)-x^2\\
\dfrac{\partial f}{\partial x} =cos(xy)*y-2x\\
\dfrac{\partial f}{\partial y} =cos(xy)*x\\
\dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f}{\partial x}}{\dfrac{\partial f}{\partial y}}\\
=- \dfrac{cos(xy)*y-2x}{cos(xy)*x}\\\\
=- \dfrac{y}{x}+ \dfrac{2}{cos(xy)} \\
[/tex]
