# What is the derivative of lnsqrtx?

I found $\frac{1}{2 x}$
Here you can use the Chain Rule to deal first with $\ln$ and then with the root to get:
$f ' \left(x\right) = \frac{1}{\sqrt{x}} \cdot \frac{1}{2 \sqrt{x}} = \frac{1}{2 x}$