Implicit differentiation and inverse trigonometric functions practice question 22

This is arcsin of a quotient. Which rules does the inside need, and would the algebra be easier in terms of $x$ before you put in $x = 2$?

Let $u = \dfrac{x}{\sqrt{1 + x^{2}}}$, so that $g' = \dfrac{u'}{\sqrt{1 - u^{2}}}$. Find $u'$ with the quotient rule, using the chain rule on $\sqrt{1 + x^{2}}$.

Simplify before substituting: $1 - u^{2} = \dfrac{1}{1 + x^{2}}$ and $u' = \dfrac{1}{(1 + x^{2})^{3/2}}$.