<s>[INST] Differentiate $y = x^{\sqrt{x}}$ (Simplification) 
I understand the gist of the problem. Just the simplification confused me.
How did $\sqrt{x}/x$ turn into $1/\sqrt{x}$?
Why does that circled 1 turn into a 2?
 [/INST] (1) $\displaystyle \sqrt{x}\cdot\frac{1}{x}=\sqrt{x}\cdot\frac{1}{(\sqrt{x})^2}=\frac{1}{\sqrt{x}}$.
(2) $\displaystyle \frac{1}{\sqrt{x}}+\frac{\ln x}{2\sqrt{x}}=\frac{2}{2}\cdot\frac{1}{\sqrt{x}}+\frac{\ln x}{2\sqrt{x}}=\frac{2}{2\sqrt{x}}+\frac{\ln x}{2\sqrt{x}}=\frac{2+\ln x}{2\sqrt{x}}$.
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