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.
Best Answer
If $y(x)= \log x$, then $y'(x)=\frac{1}{x}=e^{-y(x)}.$