Abstract
We have seen that derivatives of vector functions can be taken component by component. Consequently, much of our investigation of such derivatives reduces to the study of derivatives of real-valued functions. In this chapter we study some derivative properties for which reduction to the scalar case has an interesting variety of advantages: from being helpful (directional derivatives) to sensible (the mean value theorem) to necessary (maxima/minima).
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© 2003 Springer Science+Business Media New York
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Guzman, A. (2003). Derivatives of Scalar Functions. In: Derivatives and Integrals of Multivariable Functions. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0035-2_2
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DOI: https://doi.org/10.1007/978-1-4612-0035-2_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4274-7
Online ISBN: 978-1-4612-0035-2
eBook Packages: Springer Book Archive