[tex]~~~~~7e^{xy} +2x^2 -4y^2 =13\\\\\\\implies \dfrac{d}{dx}\left(7e^{xy} +2x^2 -4y^2\right) =\dfrac d{dx} (13)\\\\\\\implies 7\left[e^{xy} \dfrac{d}{dx} ( xy)\right] +2 \cdot 2x -4\cdot 2y \dfrac{dy}{dx} = 0\\\\\\\implies 7e^{xy} \left( x \dfrac{dy}{dx} +y\right) +4x -8y \dfrac{dy}{dx} =0\\\\\\\implies 7xe^{xy}\dfrac{dy}{dx} + 7ye^{xy} +4x -8y\dfrac{dy}{dx} = 0\\\\\\\implies \left(7xe^{xy} -8y \right) \dfrac{dy}{dx}=-7ye^{xy} -4x\\\\\\[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{-7ye^{xy} -4x}{7xe^{xy} -8y }[/tex]
