If f(x)= sin ( cos^-1((1-2^2 x)/(1+2^2 x))) and its first derivative with respect to x is -b/a log_e 2 when x=1, where a and b are integers, then the…

If $\displaystyle f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right)$ and its first derivative with respect to $\displaystyle x$ is $\displaystyle -\frac{\mathbf{b}}{\mathbf{a}} \log _{\mathrm{e}} 2$ when $\displaystyle x=1$, where a and b are integers, then the minimum value of $\displaystyle \left|\mathrm{a}^2-\mathrm{b}^2\right|$ is \_\_\_\_.