Namespaces
Variants
Actions

Difference between revisions of "Logarithmic derivative"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
 
Line 1: Line 1:
 +
{{TEX|done}}
 +
 
The derivative of the logarithm of a given function.
 
The derivative of the logarithm of a given function.
  
====Comments====
+
let $f:[a,b]\to\mathbb R$ be a positive function. Then its logarithmic derivative equals
I.e., let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060590/l0605901.png" /> be a positive function. Then its logarithmic derivative equals
+
\begin{equation*}
 
+
(\ln f)' = \frac{f'}{f}.
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060590/l0605902.png" /></td> </tr></table>
+
\end{equation*}

Latest revision as of 18:58, 7 December 2012


The derivative of the logarithm of a given function.

let $f:[a,b]\to\mathbb R$ be a positive function. Then its logarithmic derivative equals \begin{equation*} (\ln f)' = \frac{f'}{f}. \end{equation*}

How to Cite This Entry:
Logarithmic derivative. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Logarithmic_derivative&oldid=29128