**Quotients**

A natural logarithm is applied to a quotient of two functions

to transform the division into a subtraction

Differentiate by applying the chain and the sum rules

and, after rearranging, get

After multiplying out and using the common denominator formula the result is the same as if after applying the quotient rule directly to .

Read more about this topic: Logarithmic Differentiation, Applications

### Other articles related to "quotients, quotient":

Tensor Algebra -

... Because of the generality of the tensor algebra, many other algebras of interest can be constructed by starting with the tensor algebra and then imposing certain relations on the generators, i.e ... by constructing certain quotient algebras of T(V) ...

**Quotients**... Because of the generality of the tensor algebra, many other algebras of interest can be constructed by starting with the tensor algebra and then imposing certain relations on the generators, i.e ... by constructing certain quotient algebras of T(V) ...

Curiosity Quotient - Proposed Formula

... Friedman's claim is that Curiosity

... Friedman's claim is that Curiosity

**quotient**plus Passion**quotient**is greater than Intelligence**Quotient**... that the sum of a person's curiosity and passion**quotients**will always exceed their IQ ... Indeed, given the ordinal nature of psychometric**quotients**, it is not clear whether it makes sense to add the curiosity and passion**quotients**or even if ...Lehmer's GCD Algorithm - Algorithm

... Lehmer noted that most of the

... Lehmer noted that most of the

**quotients**from each step of the division part of the standard algorithm are small ... (For example, Knuth observed that the**quotients**1, 2, and 3 comprise 67.7% of all**quotients**.) Those small**quotients**can be identified from only a few leading digits ... the algorithm starts by splitting off those leading digits and computing the sequence of**quotients**as long as it is correct ...Differentiation Rules - Power Laws, Polynomials,

... Special cases If f(x) = xa, fâ˛(x) = axa â 1 when a is any real number and x is positive ... The reciprocal rule may be derived as the special case where g(x) = â1 ...

**Quotients**, and Reciprocals - Generalized Power Rule... Special cases If f(x) = xa, fâ˛(x) = axa â 1 when a is any real number and x is positive ... The reciprocal rule may be derived as the special case where g(x) = â1 ...