Reciprocal rule
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Reciprocal derivative rule
The reciprocal derivative rule differentiates 1/f(x) wherever f is differentiable and nonzero. It gives −f′(x)/[f(x)]². For example, the derivative of 1/(x²+1) is −2x/(x²+1)². This is a special case of the quotient rule and can also be derived with the chain rule.