Answer
$\dfrac{dy}{dx}=-\dfrac{y^2}{xy+1}$
Work Step by Step
Apply Implicit Differentiation Theorem: It states that for a function $F$ to be differentiable on its domain when it satisfies the following condition such that $\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$ and $F(x,y)=0$ defines $y$ as a differentiable function of $x$ and also, $F_y \ne 0$.
We are given that $F(x,y)=ye^{xy}-2$
Now, we have: $\dfrac{dy}{dx}=-\dfrac{y^2e^{xy}}{e^{xy}+yxe^{xy}}$
or, $\dfrac{dy}{dx}=-\dfrac{y^2e^{xy}}{e^{xy}(1+xy)}$
or, $\dfrac{dy}{dx}=-\dfrac{y^2}{xy+1}$
