### 4 videos in "Partial Derivatives, 2nd Derivatives, Rules, and Least Squares"

## Lecture 11: Differentials and the chain rule

Lecture 11: Differentials and the chain rule

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Part of video series Calculus 3 Course acquired through MIT OpenCourseWare

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.

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Learn about differentials and the chain rule in many variables.

- Problem Set - A problem set with some problems from this lecture.
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
- Differentiation Identities - Limit definitions of the derivative, Fundamental Theorem for Derivatives, and rules of derivatives

- What are differentials and how do you compute them?
- What is implicit differentiation?
- What is a total differential and how do you find it?
- How is df different than delta f?
- Why are differentials useful?
- What is the chain rule for differentials?
- How can you use the chain rule to find dw/dt when w = x^y + z, x = t, y = e^t, and z = sint?
- What is the product rule and quotient rule using differentials?
- How do you use the chain rule with four variables?
- How do you find df/du and df/dv if u and v depend on x and y?
- How does the chain rule work with parametric functions?
- How does the chain rule work with polar coordinates?
- What is the gradient vector and how do you find it?

Differentials are the topic in this lecture, and they are explained both in theory and in practical problems. Differentials are different than delta of the variable. This is an important lecture in understanding the theory behind topics in this course. The chain rule is discussed in depth with actual problems for functions of multiple variables.