Solve this following

If $y=\log \sqrt{\frac{1+\cos ^{2} x}{1-e^{2 x}}}$, show that $\frac{d y}{d x}=\frac{e^{2 x}}{\left(1-e^{2 x}\right)}-\frac{\sin x \cos x}{\left(1+\cos ^{2} x\right)}$