# Differentiating an Integral : Leibniz ’ Rule KC Border

@inproceedings{Border2016DifferentiatingAI, title={Differentiating an Integral : Leibniz ’ Rule KC Border}, author={Kc Border}, year={2016} }

- Published 2016

1 The vector case The following is a reasonably useful condition for differentiating a Riemann integral. The proof may be found in Dieudonné [6, 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 : Rn × Rm where a typical element of Rn × Rm is denoted (x, z) with x ∈ Rn and y ∈ Rm. The partial derivative Dxf is a Fréchet derivative with respect to x holding z fixed. 1 Theorem Let A ⊂ Rn… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-2 OF 2 CITATIONS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 10 REFERENCES

## Infinite Dimensional Analysis: A Hitchhiker's Guide

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL