If \( f(x)=\sin\!\left(\cos^{-1}\!\left(\dfrac{1-2^{2x}}{1+2^{2x}}\right)\right) \) and its first derivative with respect to \( x \) is \( -\dfrac{b}{a}\log_e 2 \) when \( x=1 \), where \( a \) and \( b \) are integers, then the minimum value of \( \left|a^{2}-b^{2}\right| \) is __________.
