- This is about a method in calculus. For other uses of "reciprocal", see reciprocal.
, the reciprocal rule
is a shorthand method of finding the derivative
of a function
that is the reciprocal
of a differentiable
function, without using the quotient rule
or chain rule
The reciprocal rule states that the derivative of is given by
From the quotient rule
The reciprocal rule is derived from the quotient rule
, with the numerator
From the chain rule
It is also possible to derive the reciprocal rule from the chain rule, by a process very much like that of the derivation of the quotient rule. One thinks of
as being the function composed with the function . The result then follows by application of the chain rule.
The derivative of is:
The derivative of (when ) is:
For more general examples, see the derivative article.