\[\bbox[yellow,5px]{\dfrac{d}{dx}\ln x = \dfrac{1}{x} }\]
Applying the Chain rule, we have
\[\dfrac{d}{dx}\ln(\text{stuff}) = \dfrac{1}{(\text{stuff})} \cdot \dfrac{d}{dx} (\text{stuff}) \]
You’ll usually see this written as
\[\dfrac{d}{dx}\ln u = \dfrac{1}{u} \cdot \dfrac{du}{dx} \]
Practice problems are of course below!
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