Logarithmic derivative

English

Pronunciation

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Noun

1. Template:Lb Given a real or complex function $f$, the ratio of the value of the derivative to the value of the function, $\frac{f^{\prime }}{f}$, regarded as a function. Template:C
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Usage notes

• The logarithmic derivative can be interpreted intuitively as the infinitesimal relative change in $f$ at any given point.
• If $f(x)$ is a differentiable function of a real variable and takes only positive values (so that $\ln f(x)$ is defined), the chain rule applies and the logarithmic derivative is equal to the derivative of the logarithm: $\frac{f^{\prime }(x)}{f(x)}=(\ln f(x))$.
• The definition above is more broadly applicable: for $f(z)$ a function of a complex variable, its logarithmic derivative will be computable so long as $f(z)\ne 0$ and $f^{\prime }(z)$ is defined.

Further reading

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