Generalization of the formula of Faa di Bruno for a composite function with a vector argument
The paper presents a new explicit formula for the nth total derivative of a composite function with a vector argument. The well-known formula of Faa di Bruno gives an expression for the nth derivative of a composite function with a scalar argument. The formula proposed represents a straightforward g...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002970 |
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| Summary: | The paper presents a new explicit formula for the nth total
derivative of a composite function with a vector argument. The
well-known formula of Faa di Bruno gives an expression for the
nth derivative of a composite function with a scalar argument.
The formula proposed represents a straightforward generalization of
Faa di Bruno's formula and gives an explicit expression for the
nth total derivative of a composite function when the argument is
a vector with an arbitrary number of components. In this sense, the
formula of Faa di Bruno is its special case. The mathematical tools
used include differential operators, polynomials, and Diophantine
equations. An example is shown for illustration. |
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| ISSN: | 0161-1712 1687-0425 |