Differentiate it as earlier as possible and explain it briefly

$\frac{\sqrt{a^2+x^2}+\sqrt{a^2-x^2}}{\sqrt{a^2+x^2}-\sqrt{a^2-x^2}}\times\frac{\sqrt{a^2+x^2}-\sqrt{a^2-x^2}}{\sqrt{a^2+x^2}-\sqrt{a^2-x^2}}=\frac{(\sqrt{a^2+x^2}-\sqrt{a^2-x^2})^2}{a^2+x^2-(a^2-x^2)}=\frac{a^2+x^2+2(a^4-x^4)+a^2-x^2}{2x^2}=\frac{2a^2+2(a^4-x^4)}{2x^2}=\frac{a^2+a^4-x^4}{x^2}=a^2x^{-2}+a^4x^{-4}-x^2$
$-2a^2x^{-1}+(-2)a^4x^{-1}-2x=-\frac{2a^2}{x}-2\frac{a^4}{x}-2x=-\frac{2(a^2+a^4+x^2)}{x}$