University Calculus III Partial Derivatives — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 5 definitions and 7 theorems, 8 worked examples, 3 diagrams, in 12 printable pages. This page lists what the notes cover. The notes themselves come with the University Calculus III bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Partial Derivatives — what the notes cover
7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
First-order partial derivatives
- Definition — Partial derivatives of a function of two variables
- Theorem — Computing a partial derivative
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Higher-order and mixed partial derivatives
- Definition — Second-order partial derivatives
- Theorem — Equality of mixed partial derivatives
Also in this section: 1 worked example, 1 note on method and common errors.
Tangent planes to a graph
- Theorem — Tangent plane to a graph
Also in this section: 1 worked example, 1 note on method and common errors.
Linear approximation and differentials
- Definition — Linearization
- Definition — Differentiable function of two variables
- Theorem — Continuous partials give differentiability
- Definition — Total differential
Also in this section: 2 worked examples, 1 note on method and common errors, 1 diagram.
The chain rule for several variables
- Theorem — Chain rule with one independent variable
- Theorem — Chain rule with two independent variables
Also in this section: 2 worked examples, 1 note on method and common errors, 1 diagram.
Implicit differentiation
- Theorem — Implicit differentiation
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Calculus III Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Partial Derivatives practice worksheet is free and stays free.
Every University Calculus III topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Calculus III units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Partial Derivatives practice worksheet About the Partial Derivatives unit test