Derivative of $$$\ln\left(x_{0}\right)$$$
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Find $$$\frac{d}{dx_{0}} \left(\ln\left(x_{0}\right)\right)$$$.
Solution
The derivative of the natural logarithm is $$$\frac{d}{dx_{0}} \left(\ln\left(x_{0}\right)\right) = \frac{1}{x_{0}}$$$:
$${\color{red}\left(\frac{d}{dx_{0}} \left(\ln\left(x_{0}\right)\right)\right)} = {\color{red}\left(\frac{1}{x_{0}}\right)}$$Thus, $$$\frac{d}{dx_{0}} \left(\ln\left(x_{0}\right)\right) = \frac{1}{x_{0}}$$$.
Answer
$$$\frac{d}{dx_{0}} \left(\ln\left(x_{0}\right)\right) = \frac{1}{x_{0}}$$$A
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