Proposition of a Recursive Formula to Calculate the Higher Order Derivative of a Composite Function without Using the Resolution of the Diophantine Equation | Chapter 11 | Advances in Mathematics and Computer Science Vol. 4
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 ...