If $2 x^{y}+3 y^{x}=20$, then $\frac{d y}{d x}$ at $(2,2)$ is equal to :

Question

$-\left(\frac{3+\log _{e} 16}{4+\log _{e} 8}\right)$

$-\left(\frac{2+\log _{e} 8}{3+\log _{e} 4}\right)$

$-\left(\frac{3+\log _{e} 8}{2+\log _{e} 4}\right)$

$-\left(\frac{3+\log _{e} 4}{2+\log _{e} 8}\right)$

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