Question

If sin(xy)=x^2, then dy/dx =

Answer 1

Hello,


`f(x,y)=sin(xy)-x^2\\ (\partial f)/(\partial x) =cos(xy)*y-2x\\ (\partial f)/(\partial y) =cos(xy)*x\\ (dy)/(dx) =-((\partial f)/(\partial x))/((\partial f)/(\partial y))\\ =- (cos(xy)*y-2x)/(cos(xy)*x)\\\\ =- (y)/(x)+ (2)/(cos(xy)) \\`