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The logarithmic derivative is then / and one can draw the general conclusion that for f meromorphic, the singularities of the logarithmic derivative of f are all simple poles, with residue n from a zero of order n, residue −n from a pole of order n. See argument principle. This information is often exploited in contour integration.
In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, [1] () ′ = ′ ′ = () ′.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
The logarithmic derivative provides a simpler expression of the last form, as well as a direct proof that does not involve any recursion. The logarithmic derivative of a function f , denoted here Logder( f ) , is the derivative of the logarithm of the function.
The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): () ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.
3.1 Proof from derivative definition and limit properties. ... 3.4 Proof by logarithmic differentiation. 4 Higher order derivatives. 5 See also. 6 References.
5.1 Proof for Taylor's theorem in one real variable. ... Logarithmic differentiation; ... repeated derivatives of ...
The derivative with a generalized functional argument f(x) is = ′ (). The quotient at the right hand side is called the logarithmic derivative of f. Computing f'(x) by means of the derivative of ln(f(x)) is known as logarithmic differentiation. [38]