
02371120
j
2007c.00384
Huang, HuangNan
Marcantognini, Stefania
Young, Nicholas
Chain rules for higher derivatives.
Math. Intell. 28, No. 2, 6169 (2006).
2006
Springer US, New York, NY
EN
I45
chain rule
directional derivatives
doi:10.1007/BF02987158
From the introduction: We define a notion of higherorder directional derivative of a smooth function and use it to establish three simple formulae for the nth derivative of the composition of two functions. These three "higher order chain rules" are alternatives to the classical Faà di Bruno formula. They are less explicit than Faà di Bruno's formula but are much simpler and avoid Diophantine or combinatorial complications.