In calculus, the quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist.
If the function one wishes to differentiate, can be written as
and, then the rule states that the derivative of is
More precisely, if all x in some open set containing the number a satisfy, and and both exist, then exists as well and
And this can be extended to calculate the second derivative as well (you can prove this by taking the derivative of twice). The result of this is:
The quotient rule formula can be derived from the product rule and chain rule.
Read more about Quotient Rule: Examples
Famous quotes containing the word rule:
“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)