Question

Dada a função cotg(xy) = 2, calcule dy/dx​

Answer 1

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$\large\boxed{\begin{array}{l}\sf cotg(xy)=2\\\sf -cossec^2(xy)\cdot\bigg[y+x\dfrac{dy}{dx}\bigg]=0\\\sf -cossec^2(xy)\cdot y-x cossec^2(xy)\cdot\dfrac{dy}{dx}=0\\\sf xcossec^2(xy)\cdot\dfrac{dy}{dx}=-ycossec^2(xy)\\\sf \dfrac{dy}{dx}=-\dfrac{y\diagup\!\!\!\!cossec^2(xy)}{x\diagup\!\!\!\!\!\!cossec^2(xy)}\\\sf\dfrac{dy}{dx}=-\dfrac{y}{x}\end{array}}$