If f(x) = sin ( cos ^(-1) ( ( 1- 2 ^(2x)...

If `f(x) = sin ( cos ^(-1) ( ( 1- 2 ^(2x))/( 1+ 2^(2x))))` and its fist derivative with respect to x is `- (b)/(a) log_(e ) 2` when x = 1, where a and b are integers, then the minimum value of `|a^(2) - b^(2) |` is `"______________"`.

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