---
title: "MVC.AQR.3: Multivariable Differentiation Overview (Georgia Mathematics standard)"
code: MVC.AQR.3
cite_as: Georgia Standards of Excellence, Mathematics, MVC.AQR.3
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/MVC.AQR.3
md_url: https://georgiahomeroom.org/standards/code/MVC.AQR.3.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/MVC.AQR.3.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# MVC.AQR.3: Multivariable Differentiation Overview

Define, describe, and represent the differentiation of functions of two independent variables and differential vectors to solve contextual, mathematical problems and to explain real-life phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- **MVC.AQR.3.1**: Approximate the partial derivatives at a point of a function defined by a table of data.
- **MVC.AQR.3.2**: Find expressions for the first and second partial derivatives of a function.
- **MVC.AQR.3.3**: Use the total differential to approximate mathematical models.
- **MVC.AQR.3.4**: Represent the partial derivatives of a system of two functions in two variables using the Jacobian.
- **MVC.AQR.3.5**: Find the partial derivatives of the composition of functions using the general chain rule.
- **MVC.AQR.3.6**: Apply partial differentiation to problems of optimization, including problems requiring the use of the Lagrange multiplier.
- **MVC.AQR.3.7**: Find the family of solutions and the envelope of the family of solutions to differential equations, including Clairaut equations.
- **MVC.AQR.3.8**: Define and apply the gradient, the divergence, and the curl in terms of differential vector operations.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.