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Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative. [ citation needed ] Logarithms can be used to remove exponents, convert products into sums, and convert division into subtraction—each of which may lead to a simplified ...
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()
If we consider functions of the form () = where is any complex number and is a complex number in a slit complex plane that excludes the branch point of 0 and any branch cut connected to it, and we use the conventional multivalued definition := (), then it is straightforward to show that, on each branch of the complex logarithm, the same ...
In number theory, the Lagarias arithmetic derivative or number derivative is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis.
Let f denote a real-valued function defined on a subset I of the real numbers.. If a ∈ I is a limit point of I ∩ [a,∞) and the one-sided limit + ():= + () exists as a real number, then f is called right differentiable at a and the limit ∂ + f(a) is called the right derivative of f at a.
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] () ′ = ′ ′ = () ′.