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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] () ′ = ′ ′ = () ′.
For example, since the logarithm of a product is the sum of the logarithms of the factors, we have () ′ = ( + ) ′ = () ′ + () ′. So for positive-real-valued functions, the logarithmic derivative of a product is the sum of the logarithmic derivatives of the factors.
5 Example. 6 Converse of the one ... Download as PDF; Printable version; In other projects ... Logarithmic differentiation; Related rates; Taylor's theorem; Rules and ...
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
2 Examples. 3 Convergence of products. ... Download as PDF; Printable version; ... Implicit differentiation; Logarithmic differentiation;
The second example illustrates the following generalization of Rolle's theorem: Consider a real-valued, continuous function f on a closed interval [ a , b ] with f ( a ) = f ( b ) .
Using that the logarithm of a product is the sum of the logarithms of the factors, the sum rule for derivatives gives immediately = = (). The last above expression of the derivative of a product is obtained by multiplying both members of this equation by the product of the f i . {\displaystyle f_{i}.}
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 ...