L'Hôpital's rule

In calculus (an area of mathematics), L'Hôpital's rule uses derivatives to determine otherwise hard to compute limitss. If you are trying to determine the limit of some quotient f(x)/g(x), and both the numerator and denominator approach 0 or infinity, then differentiate numerator and denominator and determine the limit of the quotient of the derivatives. If that limit exists, the rule states that it will be the same as the original limit.

That is,

given

For example, a case of "0/0":

and a case of "∞/∞":

Sometimes, even limits which don't appear to be quotients can be handled with the same rule:

The rule is named after the 17th century French mathematician Guillaume François Antoine, Marquis de l'Hôpital (1661 - 1704), who published the rule in his book Analyse des infiniment petits pour l'intelligence des lignes courbes (1692), the first textbook to be written on the differential calculus.