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4 Logarithmic functions. ... Printable version; ... This is the definition of the derivative. All differentiation rules can also be reframed as rules involving limits.
Intuitively, one may think of as the logarithm of some element of , in which case, this condition is analogous to the ordinary chain rule. However, F {\displaystyle F} is not necessarily equipped with a unique logarithm; one might adjoin many "logarithm-like" extensions to F . {\displaystyle F.}
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 ...
It can also be useful when applied to functions raised to the power of variables or functions. Logarithmic differentiation relies on the chain rule as well as properties of logarithms (in particular, the natural logarithm, or the logarithm to the base e) to transform products into sums and divisions into subtractions.
These are the three main logarithm laws/rules/principles, [3] from which the other properties listed above can be proven. Each of these logarithm properties correspond to their respective exponent law, and their derivations/proofs will hinge on those facts. There are multiple ways to derive/prove each logarithm law – this is just one possible ...
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