Standard #: 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.

Related Courses

Course Number1111 Course Title222
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Resources

Tutorials

Name Description
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

Tutorials

Name Description
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.



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