Chain rule for higher derivatives
From Calculus
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 |
---|---|
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). |