Question

Encontre dy/dx por diferenciação implícita 3x² y+5xy²=xy

Answer 1

$\sf{3x^2y+5xy^2=xy}\\\sf{6xy+3x^2\dfrac{dy} {dx}+5y^2+10xy\dfrac{dy}{dx}=y+x\dfrac{dy}{dx}}\\\sf{3x^2\dfrac{dy}{dx}+10xy\dfrac{dy}{dx}-x\dfrac{dy}{dx}=-6xy-5y^2+y}\\\sf{\dfrac{dy}{dx}(3x^2+10xy-x)=-6xy-5y^2+y}\\\boxed{\boxed{\boxed{\boxed{\sf{\dfrac{dy}{dx}=\dfrac{-6xy-5y^2+y}{3x^2+10xy-x}}}}}}$