<s>[INST] Finding the derivative of $\sqrt{x+\sqrt{x^2+5}}$ How to derive $y=\sqrt{x+\sqrt{x^2+5}}$ at $x=2$.I used logarithmic differentiation and chain rule over and over again but I can't get the right answer 
 [/INST] \begin{align*}
\frac{d}{dx}y & = \frac{d}{dx}\sqrt{x+\sqrt{x^2+5}}\\
& = \frac{1}{2}\frac{1}{\sqrt{x+\sqrt{x^2+5}}}\cdot \frac{d}{dx}(x+\sqrt{x^2+5})\\
& = \frac{1}{2}\frac{1}{\sqrt{x+\sqrt{x^2+5}}} \,\left(1+\frac{x}{\sqrt{x^2+5}}\right)\\
\end{align*}
Now simplify as best as you can.
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