alexa Differentiating an Integral: Leibniz’ Rule
Bioinformatics & Systems Biology

Bioinformatics & Systems Biology

Journal of Theoretical and Computational Science

Author(s): KC Border

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The following is a reasonably useful condition for differentiating a Riemann integral. The proof may be found in Dieudonné [5, Theorem 8.11.2, p. 177]. One thing you have to realize is that for Dieudonné a partial derivative can be taken with respect to a vector variable. That is, if f : R n × R m where a typical element of R n × R m is denoted (x, z) with x ∈ R n and y ∈ R m. The partial derivative Dxf is a Fréchet derivative with respect to x holding z fixed.

This article was published in Division of the Humanities and Social Sciences and referenced in Journal of Theoretical and Computational Science

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