Standard 2 : Develop an understanding for and determine derivatives.



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General Information

Number: MA.912.C.2
Title: Develop an understanding for and determine derivatives.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Calculus

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.C.2.1: State, understand and apply the definition of derivative. Apply and interpret derivatives geometrically and numerically.
MA.912.C.2.2: Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.
MA.912.C.2.3: Prove the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule.
Clarifications:
Clarification 1: Special cases of rules include a constant multiple of a function and the power of a function.
MA.912.C.2.4: 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.
Clarifications:
Clarification 1: Special cases of rules include a constant multiple of a function and the power of a function.
MA.912.C.2.5: Find the derivatives of implicitly defined functions.
MA.912.C.2.6: Find derivatives of inverse functions.
MA.912.C.2.7: Find second derivatives and derivatives of higher order.
MA.912.C.2.8: Find derivatives using logarithmic differentiation.
MA.912.C.2.9: Demonstrate and use the relationship between differentiability and continuity.
MA.912.C.2.10: Apply the Mean Value Theorem.


Related Resources

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

Tutorials

Name Description
Calculus: Derivatives 1:

In this video we will learn through an example, that a derivative is simply the slope of a curve at any given point.

Calculating Slope of Tangent Line Using Derivative Definition:

In this video we will find the slope of the tangent line using the formal definition of derivative.

Mean Value Theorem:

We will learn the meaning of the Mean Value Theorem.

Derivative as Slope of a Tangent Line:

We will find the derivative of a function by finding the slope of the tangent line.

Mean Value Theorem:

In this video we will take an in depth look at the Mean Value Theorem.

The Derivative of f(x)=x^2 for Any x:

In this video we will find the derivative of a function based on the slope of the tangent line.

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.

The Product Rule for Derivatives:

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

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.

Derivative of Log with Arbitrary Base:

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

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.

Chain Rule Introduction:

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

Chain Rule Definition and Example:

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

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.

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.



Student Resources

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

Tutorials

Title Description
Calculus: Derivatives 1:

In this video we will learn through an example, that a derivative is simply the slope of a curve at any given point.

Calculating Slope of Tangent Line Using Derivative Definition:

In this video we will find the slope of the tangent line using the formal definition of derivative.

Mean Value Theorem:

We will learn the meaning of the Mean Value Theorem.

Derivative as Slope of a Tangent Line:

We will find the derivative of a function by finding the slope of the tangent line.

Mean Value Theorem:

In this video we will take an in depth look at the Mean Value Theorem.

The Derivative of f(x)=x^2 for Any x:

In this video we will find the derivative of a function based on the slope of the tangent line.

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.

The Product Rule for Derivatives:

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

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.

Derivative of Log with Arbitrary Base:

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

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.

Chain Rule Introduction:

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

Chain Rule Definition and Example:

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

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.

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.