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 ![]() ![]() ![]() |
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1 | ![]() |
2 | ![]() |