Вычислить 2ю производную y'' a=const

Решите задачу:

$y=a^2ln(x+\sqrt{a^2+x^2})-x\sqrt{a^2-x^2}\\\\y'=a^2\cdot \frac{1+\frac{2x}{2\sqrt{a^2+x^2}}}{x+\sqrt{a^2+x^2}}-\sqrt{a^2-x^2}-\frac{x\cdot (-2x)}{2\sqrt{a^2-x^2}}=\\\\=a^2\cdot \frac{\sqrt{a^2+x^2}+x}{\sqrt{a^2+x^2}(x+\sqrt{a^2+x^2})}-\frac{a^2-x^2-x^2}{\sqrt{a^2-x^2}}=\frac{a^2}{\sqrt{a^2+x^2}}-\frac{a^2-2x^2}{\sqrt{a^2-x^2}}\\\\y''=\frac{-a^2\cdot \frac{2x}{2\sqrt{a^2+x^2}}}{a^2+x^2}-\frac{-4x\sqrt{a^2-x^2}-(a^2-2x^2)\cdot \frac{-2x}{2\sqrt{a^2-x^2}}}{a^2-x^2}=\\\\=\frac{-a^2x}{\sqrt{(a^2+x^2)^3}}+$

$+\frac{2x^3-3xa^2}{\sqrt{(a^2-x^2)^3}}$