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Logarithmic derivative | mathematical analysis | advanced level
10 months ago
22
Health & Science
mathematics
mathematical analysis
calculus
derivative
differentiate
differentiation
product rule
logarithm
logarithmic derivative
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.
#Mathematics #MathematicalAnalysis #Calculus
The same video on YouTube:
https://youtu.be/7HeMgZrN8zY
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