MAFS.912.C.2.5Archived Standard

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Find the derivatives of composite functions using the Chain Rule.

Remarks

Example 1: Find  for .

Example 2: Find for .
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Differential Calculus - Develop an understanding of the derivative as an instantaneous rate of change, using geometrical, numerical, and analytical methods. Use this definition to find derivatives of algebraic and transcendental functions and combinations of these functions (using, for example, sums, composites, and inverses). Find second and higher order derivatives. Understand and use the relationship between differentiability and continuity. Understand and apply the Mean Value Theorem. Find derivatives of algebraic, trigonometric, logarithmic, and exponential functions. Find derivatives of sums, products, and quotients, and composite and inverse functions. Find derivatives of higher order, and use logarithmic differentiation and the Mean Value Theorem.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived

Related Courses

This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Tutorials

Using the Product Rule and the Chain Rule:

In this video we will use the chain rule and the product rule together to find a derivative of a composite function.

Type: Tutorial

Chain Rule Introduction:

This video is an introduction on how to apply the chain rule to find the derivative of a composite function.

Type: Tutorial

Chain Rule Definition and Example:

In this video we will define the chain rule and use it to find the derivative of a function.

Type: Tutorial

Chain Rule With Triple Composition:

We will use the chain rule to find the derivative of a triple-composite function.

Type: Tutorial

Chain Rule Example Using Visual Information:

In this video we will analyze the graph of a function and its tangent line, then use the chain rule to find the value of the derivative at that point.

Type: Tutorial

Chain Rule Example Using Visual Function Definitions:

We will use the chain rule to find the value of a composite function at a given point, given the graphs of the two composing functions.

Type: Tutorial

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Tutorials

Using the Product Rule and the Chain Rule:

In this video we will use the chain rule and the product rule together to find a derivative of a composite function.

Type: Tutorial

Chain Rule Introduction:

This video is an introduction on how to apply the chain rule to find the derivative of a composite function.

Type: Tutorial

Chain Rule Definition and Example:

In this video we will define the chain rule and use it to find the derivative of a function.

Type: Tutorial

Chain Rule With Triple Composition:

We will use the chain rule to find the derivative of a triple-composite function.

Type: Tutorial

Chain Rule Example Using Visual Information:

In this video we will analyze the graph of a function and its tangent line, then use the chain rule to find the value of the derivative at that point.

Type: Tutorial

Chain Rule Example Using Visual Function Definitions:

We will use the chain rule to find the value of a composite function at a given point, given the graphs of the two composing functions.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.