Logarithmic derivative

In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula

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${\displaystyle f(a)-f(b)=\int _{b}^{a}f'(t)\,dt}$
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where ${\displaystyle f'}$ is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely ${\displaystyle f',}$ scaled by the current value of f.

When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f. This follows directly from the chain rule: