The Leibniz rule for differentiation of a definite integral is discussed. Alternative methods of proof are given. The result is generalised to an arbitrary number of dimensions with special cases of a surface and volume integral given as examples.
%0 Journal Article
%1 1973
%A Flanders, Harley
%D 1973
%I Mathematical Association of America
%J The American Mathematical Monthly
%K integral mathematics
%N 6
%P 615-627
%R 10.2307/2319163
%T Differentiation Under the Integral Sign
%U http://www.jstor.org/stable/2319163
%V 80
%X The Leibniz rule for differentiation of a definite integral is discussed. Alternative methods of proof are given. The result is generalised to an arbitrary number of dimensions with special cases of a surface and volume integral given as examples.