Logarithmic derivative

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula $${\displaystyle {\frac {f'}{f}}}$$ where ${\displaystyle f'}$ is the derivative of f.^[1] 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:^[1] $${\displaystyle {\frac {d}{dx}}\ln f(x)={\frac {1}{f(x)}}{\frac {df(x)}{dx}}}$$