Difference between revisions of "Chain rule for higher derivatives"
From Calculus
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==Statement== | ==Statement== | ||
Latest revision as of 13:56, 5 September 2011
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.
View other differentiation rules
Statement
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 .
Particular cases
Value of | Formula for derivative of at |
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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). |