About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Computation of Derivatives 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:
- Overview of computing derivatives
- Calculations with constant and polynomial functions
- Computing derivatives of differences, products, sums and more
- Calculating derivatives of exponential, logarithmic, trig functions and more
- Computations with higher order derivatives and absolute value functions
- Understanding implicit differentiation and using the chain rule
- Using substitution with difficult integrals
- Computing derivatives with logarithmic differentiation
- Finding derivatives of polar, vector and parametric functions
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1. How to Compute Derivatives
This lesson briefly reviews what the derivative of a function is. Then we will look at the limit definition of a derivative, use it to compute derivatives, and see a few shortcuts that result from the limit definition of derivatives.
2. Calculating Derivatives of Constant Functions
In calculus, one of the primary tasks is to find the derivative of a function. Different types of functions require different techniques to find their derivative. This lesson will cover the simple process to find derivatives of constant functions.
3. Calculating Derivatives of Polynomial Equations
Polynomials can describe just about anything and are especially common in describing motion. Learn the tricks to quickly finding the derivatives of these ubiquitous functions.
4. Finding Derivatives of Sums, Products, Differences & Quotients
This lesson will go over how to find the derivative of a sum, difference, product, and quotient. We will look at the different formulas involved in these derivatives and use those formulas to calculate some derivatives.
5. Calculating Derivatives of Exponential Equations
Earth's population is booming! But why is the population increasing so much more drastically than it did many years ago? In this lesson, learn how to calculate the rates of change in exponentials by discovering the rules of derivatives with exponents.
6. Calculating Derivatives of Logarithmic Functions
Logarithms appear in all types of applications like carbon dating, brightness of stars and musical acoustics. In this lesson we explore how to calculate the derivative of logarithmic functions.
7. Calculating Derivatives of Trigonometric Functions
The trigonometric functions show up almost everywhere that you have a repeating pattern. In this lesson, learn how to find the derivatives of the trigonometric functions.
8. How to Calculate Derivatives of Inverse Trigonometric Functions
Like a metronome, trigonometric functions are regular. Even predictable. In this lesson, you will learn how to use this predictability to remember the derivative formulas for these common functions.
9. Calculating Derivatives of Absolute Value Functions
A fundamental distance measure in math, science, and engineering is the absolute value. In this lesson, we will explore the differentiation of absolute value functions.
10. Calculating Higher Order Derivatives
Differentiating functions doesn't have to stop with the first or even second derivative. Learn what a mathematical jerk is as you calculate derivatives of any order in this lesson.
11. Implicit Differentiation: Examples & Formula
This lesson takes you through the method of implicit differentiation. Implicit differentiation utilizes all of your basic derivative rules to find the derivative of equations that are not in standard form.
12. Substitution Techniques for Difficult Integrals
Up, down. East, West. Opposites are everywhere. In this lesson, learn how you can think of substitution for integration as the opposite of the chain rule of differentiation.
13. Using the Chain Rule to Differentiate Complex Functions
If you've ever seen a complicated function, this lesson is for you. Most functions that we want to differentiate are complicated functions, for which no single derivative rule will work. In this lesson, learn how to use the chain rule to simplify nesting equations.
14. Using Logarithmic Differentiation to Compute Derivatives
In this lesson, we will explore logarithmic differentiation and show how this technique relates to certain types of functions. Using two examples, we will learn how to compute derivatives using this differentiation method.
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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: Concept of the Derivative
- Saxon Calculus: Derivative at a Point
- Saxon Calculus: Derivative as a Function
- Saxon Calculus: Second Derivatives
- Saxon Calculus: Applications of the Derivative
- 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