If $x^y\; y^x = 100$, evaluate $\large \frac{dy}{dx}$

Question

$\begin{array}{1 1}(A) \large \bigg (\Large \frac{\Large \frac{x}{y} + \log y}{\Large \frac{y}{x} + \log x} \bigg) \\ (B) \large \bigg (\Large \frac{\Large \frac{y}{x} + \log x}{\Large \frac{x}{y} + \log y} \bigg) \\ (C) \large \bigg (\Large \frac{\Large \frac{x}{y} + \log x}{\Large \frac{y}{x} + \log y} \bigg) \\(D) \large \bigg (\Large \frac{\Large \frac{y}{x} + \log y}{\Large \frac{x}{y} + \log x} \bigg) \end{array}$