*The formula of Fa`a Di Bruno provides a
powerful tool to calculate the higher order derivative of a composite function.
Unfortunately it has three weaknesses: it is not a recursive formula, it
totally depends on the resolution of the diophantine equation and a change in
the order of the derivative requires the total change of the calculation. With
these weaknesses and the absence of a formula to program, Fa`a Di Bruno’s formula
is less useful for formal computation.*

*Other complicated techniques based on
ﬁnite diﬀerence calculation (see [1]) are recursive, however the complexity of
the calculation algorithm is very high. There is as well some techniques based on
graphs (see [2]) to calculate the coeﬃcients to a certain order, but without
giving the general formula.*

*In our work we propose a new formula to calculate the higher order derivative of a composite function gof. It is of great interest, because it is recursive and it is not based on the resolution of the diophantine equation. We complete this work by giving an expression that allows to ﬁnd directly the n-th derivative of a composite function.*

**Author(s) Details**

**Dr. El Khomssi Mohammed**

*Modelling and Scientiﬁc Computing Laboratory, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco.*

**Dr. Chaachoui Ghizlane**

*Modelling and Scientiﬁc Computing Laboratory, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco.*

**Dr. Ez-Zriouli Rachid**

*Modelling and Scientiﬁc Computing Laboratory, Faculty of Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco.*

**View Volume: **http://bp.bookpi.org/index.php/bpi/catalog/book/97

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