In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula
where f ′ is the derivative 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 derivative of the natural logarithm of f. This follows directly from the chain rule.
Read more about Logarithmic Derivative: Basic Properties, Computing Ordinary Derivatives Using Logarithmic Derivatives, Integrating Factors, Complex Analysis, The Multiplicative Group, Examples
Famous quotes containing the word derivative:
“Poor John Field!—I trust he does not read this, unless he will improve by it,—thinking to live by some derivative old-country mode in this primitive new country.... With his horizon all his own, yet he a poor man, born to be poor, with his inherited Irish poverty or poor life, his Adam’s grandmother and boggy ways, not to rise in this world, he nor his posterity, till their wading webbed bog-trotting feet get talaria to their heels.”
—Henry David Thoreau (1817–1862)