Final answer to the problem
$(\left(\frac{d}{dx}\right)^2\left(x\right)\left(x^2+\sqrt{x^2+1}\right)$
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1
Apply the property of the quotient of two powers with the same exponent, inversely: $\frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m$, where $m$ equals $2$
$(\left(\frac{d}{dx}\right)^2\left(x\right)\left(x^2+\sqrt{x^2+1}\right)$
Final answer to the problem
$(\left(\frac{d}{dx}\right)^2\left(x\right)\left(x^2+\sqrt{x^2+1}\right)$