Question

Find dy/dx by implicit differentiation. 2y - x + xy = 3 1-Y 2 + x X + 2 X + 2 O y+1 X + 2

Answer 1

Let's do the implicit differentiation:

$\begin{gathered} \frac{d}{dx}(2y-x+xy)=\frac{d}{dx}3 \\ \frac{d}{dx}(2y)-\frac{d}{dx}x+\frac{d}{dx}(xy)=0 \\ 2\frac{dy}{dx}-1+(y+x\frac{dy}{dx})=0 \\ 2\frac{dy}{dx}+x\frac{dy}{dx}=1-y \\ (2+x)\frac{dy}{dx}=1-y \\ \frac{dy}{dx}=\frac{1-y}{2+x} \end{gathered}$

Therefore, the answer is the first one.