Calculus Revisited: Multivariable Calculus (Res.18-007, MIT OCW). This consists of 26 video lectures taught by
Professor Herbert Gross, on a study of the calculus of functions of several variables (vector arithmetic and vector calculus).
Calculus Revisited is a series of videos and related resources that covers the materials normally found in
freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series,
consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way
for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for
the first time. (from ocw.mit.edu)
Part III, Lecture 5 - Integrals Involving Parameters
Herb Gross show how the chain rule is involved in finding some integrals involving parameters. He computes the derivatives of integrals with constant limits, as well as derivatives of integrals with variable limits of integration (chain rule).