If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y) =a^2-b^2$, where $a>b>0$, then at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right), \frac{d y}{d x}=$

If $f(x)=x^{\sec ^{-1} x}$, then $f^{\prime}(2)=$

If $y=\tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\tan ^{-1}\left(\frac{7 x}{1-12 x^2}\right)$, then at $x=0, \frac{d y}{d x}=$

If $y=\sqrt{\frac{x^4 \sqrt{3 x-5}}{\left(x^2-3\right)(2 x-3)}}$, then $\left(\frac{d y}{d x}\right)_{x=2}=$