MA.912.C.2.4

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Apply the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule to solve problems with functions limited to algebraic, trigonometric, inverse trigonometric, logarithmic and exponential.

Examples

Example: Find begin mathsize 12px style fraction numerator d y over denominator d x end fraction end style for the function y=ln x. 

Example: Show that the derivative of f(x)=tan x is begin mathsize 12px style f to the power of apostrophe left parenthesis x right parenthesis space equals space s e c squared x end style using the quotient rule for derivatives. 

Example: FindError converting from MathML to accessible text..

Clarifications

Clarification 1: Special cases of rules include a constant multiple of a function and the power of a function.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Calculus
Standard: Develop an understanding for and determine derivatives.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 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

The Product Rule for Derivatives:

In this video will will apply the product rule to find the derivative of two functions.

Type: Tutorial

Product Rule for More Than Two Functions:

In this video, we will use the product rule to find the derivative of the product of three functions.

Type: Tutorial

Derivative of Log with Arbitrary Base:

In this video, we will find the derivative of a log with an arbitrary base.

Type: Tutorial

Chain Rule for Derivative of 2^x:

Here we will see how the chain rule is used to find the derivative of a logarithmic 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 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

The Product Rule for Derivatives:

In this video will will apply the product rule to find the derivative of two functions.

Type: Tutorial

Product Rule for More Than Two Functions:

In this video, we will use the product rule to find the derivative of the product of three functions.

Type: Tutorial

Derivative of Log with Arbitrary Base:

In this video, we will find the derivative of a log with an arbitrary base.

Type: Tutorial

Chain Rule for Derivative of 2^x:

Here we will see how the chain rule is used to find the derivative of a logarithmic 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 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.