High Quality Content by WIKIPEDIA articles! Reynolds` transport theorem (also known as the Leibniz-Reynolds` transport theorem), or in short Reynolds theorem, is a three-dimensional generalization of the Leibniz integral rule which is also known as differentiation under the integral sign. The theorem is named after Osborne Reynolds (1842–1912). It is used to recast derivatives of integrated quantities and is useful in formulating the basic equations of continuum mechanics.