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If $f(x) = \sin\left(\cos^{-1}\left(\frac{1-2^{2x}}{1+2^{2x}}\right)\right)$ and its first derivative with respect to $x$ is $-\frac{b}{a}\log_e 2$ when $x = 1$, where $a$ and $b$ are integers, then the minimum value of $|a^2 - b^2|$ is ____.
$f’(1) = \frac{-12}{25}\ln 2$. So $a = 25, b = 12$ and $|a^2 - b^2| = 625 - 144 = 481$.
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