Question: Compute the following and simplify

(a) Compute and simplify:

\[\frac{d}{dx}\left( \frac{x}{\sqrt{{{x}^{2}}+2}} \right)\]

(b) Compute and simplify:

\[\int{\frac{xdx}{\sqrt{{{x}^{2}}+2}}}\]

(c) Compute the exact value:

\[\int\limits_{0}^{2}{\frac{xdx}{\sqrt{{{x}^{2}}+2}}}\]