Higher Derivatives and Differentials

  • Rodney Coleman
Part of the Universitext book series (UTX)


Let \(O \subset {\mathbb{R}}^{n}\) be open and f a real-valued function defined on O. If the function \(\frac{\partial f} {\partial {x}_{i}}\) is defined on O, then we can consider the existence of its partial derivatives. If \(\frac{\partial } {\partial {x}_{j}}( \frac{\partial f} {\partial {x}_{i}})(a)\) exists, then we write for this derivative \(\frac{{\partial }^{2}f} {\partial {x}_{j}\partial {x}_{i}}(a)\) if ij, and \(\frac{{\partial }^{2}f} {\partial {x}_{i}^{2}} (a)\) if i = j.

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Rodney Coleman
    • 1
  1. 1.Laboratoire Jean KuntzmannGrenobleFrance

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