Editing Logarithmic derivative (section)

{{Short description|Mathematical operation in calculus}}
{{More citations needed|date=August 2021}}{{Calculus}}

In [[mathematics]], specifically in [[calculus]] and [[complex analysis]], the '''logarithmic derivative''' of a [[function (mathematics)|function]] ''f'' is defined by the formula
<math display="block"> \frac{f'}{f} </math>
where <math>f'</math> is the [[derivative]] of ''f''.<ref name=":0">{{Cite web|date=7 December 2012|title=Logarithmic derivative - Encyclopedia of Mathematics|url=http://encyclopediaofmath.org/index.php?title=Logarithmic_derivative&oldid=29128| access-date=12 August 2021|website=encyclopediaofmath.org}}</ref> Intuitively, this is the infinitesimal [[relative change]] in ''f''; that is, the infinitesimal absolute change in ''f,'' namely <math>f',</math> scaled by the current value of ''f.''

When ''f'' is a function ''f''(''x'') of a real variable ''x'', and takes [[real numbers|real]], strictly [[Positive number|positive]] values, this is equal to the derivative of ln(''f''), or the [[natural logarithm]] of ''f''. This follows directly from the [[chain rule]]:<ref name=":0" />
<math display="block"> \frac{d}{dx}\ln f(x) = \frac{1}{f(x)} \frac{df(x)}{dx} </math>