Answer
$y=-x+2.$
Work Step by Step
$\dfrac{d}{dx}(xy)=\dfrac{d}{dx}(1)\rightarrow$
$y+\dfrac{dy}{dx}(x)=0\rightarrow\dfrac{dy}{dx}=-\dfrac{y}{x}.$
At $(1, 1)\rightarrow\dfrac{dy}{dx}=-\dfrac{1}{1}=-1.$
Equation of tangent:
$(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-1)=-(x-1)\rightarrow y=-x+2.$
