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 . Then,
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.
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