Chain rule for higher derivatives
This article is about a differentiation rule, i.e., a rule for differentiating a function expressed in terms of other functions whose derivatives are known.
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Suppose is a natural number, and and are functions such that is times differentiable at and is times differentiable at . Then, is times differentiable at . Further, the value of the derivative is given by a complicated formula involving compositions, products, derivatives, evaluations, and sums that depends on .
|Value of||Formula for derivative of at|
|1||(this is the chain rule for differentiation)|
|2||(obtained by using the chain rule for differentiation twice and using the product rule for differentiation).|