derivation of the quotient rule

The quotient rule is used to take the derivative of a function with divided expressions:

It is possible to prove this rule by utilizing the definition of the derivative; however, this is not nearly as elegant as the following simple proofs which use other derivative properties instead.

product rule

logarithm

logarithmic proofs

As well as being used in the proof of the quotient rule, logarithms can also be used to prove a couple of other derivative rules.

power rule

product rule