Does the logarithm satisfy any differential equation? The exponential function $\exp:\mathbb{R}\to\mathbb{R}_+$ satisfies the differential equation $f^\prime(x)=f(x)$.
Does the logarithm $\log:\mathbb{R}_+\to\mathbb{R}$ also satisfy any differential equation?
Curious about if this gets closed immediately or not... seems like a way too basic question, but I have been totally stuck with this since yesterday.

Since $\ln x:=\int_1^x\frac1t\operatorname dt$, apply FTC.  Get $\ln' x=\frac1x$.
So, $\boxed{f'(x)=\frac 1x}$.
