About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Concept of the Derivative chapter of your textbook.
- Watch fun videos that cover the calculus concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.
You'll learn all of the calculus topics covered in the textbook chapter, including:
- Graphical representations of derivatives
- How to calculate a derivative using limits
- Formula for finding instantaneous rate of change of a function
- How to prove the difference and sum rules
- Use of rules of differentiation to calculate a derivative
- How to find differentials of functions
- Definition of 'differentiable'
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1. Derivatives: Graphical Representations
Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.
2. Using Limits to Calculate the Derivative
If you know the position of someone as a function of time, you can calculate the derivative -- the velocity of that person -- as a function of time as well. Use the definition of the derivative and your knowledge of limits to do just that in this lesson.
3. Finding Instantaneous Rate of Change of a Function: Formula & Examples
In this lesson, you will learn about the instantaneous rate of change of a function, or derivative, and how to find one using the concept of limits from Calculus.
4. Proving the Sum & Difference Rules for Derivatives
Proving a derivative rule leads to a better understanding of differentiating. In this lesson we show how to prove the sum and difference rules for derivatives.
5. Applying the Rules of Differentiation to Calculate Derivatives
In this lesson, we'll review common derivatives and their rules, including the product, quotient and chain rules. We'll also examine how to solve derivative problems through several examples.
6. Finding Differentials of Functions: Definition & Examples
Differentials are equations for tangent lines to a curve on a graph. In this lesson, we will discuss what a differential is and work some examples finding differentials of various functions.
7. What It Means To Be 'Differentiable'
Lots of jets can go from zero to 300 mph quickly, but super-jets can do this instantaneously. In this lesson, learn what that means for differentiability.
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Other chapters within the Saxon Calculus Homeschool: Online Textbook Help course
- Saxon Calculus: Real Numbers
- Saxon Calculus: Algebra
- Saxon Calculus: Algebra Theorems
- Saxon Calculus: Geometry
- Saxon Calculus: Logic
- Saxon Calculus: Trigonometry
- Saxon Calculus: Graphing Calculator
- Saxon Calculus: Basics of Functions
- Saxon Calculus: Graphing Functions & Equations
- Saxon Calculus: Analysis of Graphs
- Saxon Calculus: Limits of Functions
- Saxon Calculus: Asymptotic & Unbounded Behavior
- Saxon Calculus: Continuity as a Property of Functions
- Saxon Calculus: Parametric, Polar & Vector Functions
- Saxon Calculus: Derivative at a Point
- Saxon Calculus: Derivative as a Function
- Saxon Calculus: Second Derivatives
- Saxon Calculus: Applications of the Derivative
- Saxon Calculus: Computation of Derivatives
- Saxon Calculus: Riemann Sums
- Saxon Calculus: Interpretations & Properties of Definite Integrals
- Saxon Calculus: Applications of Integrals
- Saxon Calculus: Fundamental Theorem of Calculus
- Saxon Calculus: Techniques of Antidifferentiation
- Saxon Calculus: Applications of Antidifferentiation
- Saxon Calculus: Numerical Approximation of Definite Integrals
- Saxon Calculus: Concept of Series
- Saxon Calculus: Series of Constants
- Saxon Calculus: Taylor Series