Find $\large\frac{dy}{dx}$ of the function $(\cos x)^{\large y} = (\cos y)^{\large x}$

Question

$\begin{array}{1 1}\large\frac{y\tan x+\log\cos y}{x\tan y+\log \cos x} \\ \large\frac{y\tan x-\log\cos y}{x\tan y+\log \cos x} \\ \large\frac{x\tan x+\log\cos y}{x\tan y+\log \cos x} \\ \large\frac{y\tan x+\log\cos y}{x\tan y+\log \sin x} \end{array} $