Question

EXERCÍCIO 4
Dada a função cotg(xy) = 2, calcule dy/dx
pffff reupi plisx​

Answer 1

$\cot(xy)=2\\\\\frac{d}{dx}[\cot(xy)]=\frac{d}{dx}(2)\\\\\frac{d}{d(xy)}[\cot(xy)].\frac{d}{dx}(xy)=0\\\\-\csc^2(xy).(y+x.\frac{dy}{dx})=0\\\\-y.\csc^2(xy)-x.\frac{dy}{dx}.\csc^2(xy)=0\\\\x.\frac{dy}{dx}.\csc^2(xy)=-y.\csc^2(xy)\\\\\frac{dy}{dx}=\frac{-y.\csc^2(xy)}{x.\csc^2(xy)}\\\\\frac{dy}{dx}=\frac{-y}{x}$