In this lesson on differentials and the chain rule, we learn about a new tool called the total differential, which includes all the contributions that can cause the value of a function to change. We also explore how to think of differentials as placeholders to put values and obtain tangent approximation formulas. The chain rule is introduced as a way to find the rate of change of a function on a new variable in terms of its derivatives and the dependence between the variables. Examples are given to demonstrate how to apply these concepts in calculations.
Learn about differentials and the chain rule in many variables.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.