Standard #: MAFS.912.C.2.4 (Archived Standard)


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Find the derivatives of sums, products, and quotients.


Remarks


Example 1: Find the derivative of the function f(x)= xcos(x).

Example 2: Using the quotient rule for derivatives, show that the derivative of f(x) = tan(x) is f '(x) = .

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Calculus
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 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived

Related Courses

Course Number1111 Course Title222
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 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.

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.



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