Question

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

Answer 1

Hello,

$f(x,y)=sin(xy)-x^2\\ \dfrac{\partial f}{\partial x} =cos(xy)*y-2x\\ \dfrac{\partial f}{\partial y} =cos(xy)*x\\ \dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f}{\partial x}}{\dfrac{\partial f}{\partial y}}\\ =- \dfrac{cos(xy)*y-2x}{cos(xy)*x}\\\\ =- \dfrac{y}{x}+ \dfrac{2}{cos(xy)}$