Logarithmic derivative | mathematical analysis | advanced level

Episode 109.

Logarithmic derivative | mathematical analysis | advanced level.

Branch of mathematics: mathematical analysis.
Difficulty level: advanced.

The logarithmic derivative of a function is defined as $ld(f)(x) = \frac{f'(x)}{f(x)}$.

Theorem. For any 2 functions $f$ and $g$, we have $ld(f \cdot g) = ld(f) + ld(g)$.

Theorem. For any function $f$ (taking only positive values so that $ln(f(x))$ is well-defined), we have $(ln(f(x)))' = ld(f)$.

Mathematics. Mathematical analysis. Calculus.
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