About This Chapter
Calculation of Derivatives - Chapter Summary
Our expert instructors can help you get up to speed on the calculation of derivatives in this informative chapter. When you review these lessons, you'll study the linear properties of a derivative and how to calculate derivatives of trigonometric functions. After completing this chapter, you should also be able to:
- Calculate the derivatives of inverse trigonometric functions
- Find the derivative of a polynomial equation
- Differentiate factored polynomials using the product rule
- Find derivatives of implicit functions
- Use formulas to calculate derivatives of exponential equations
- Take the derivative of tan(x) and log(x)
- Calculate higher order derivatives
You can tackle even the toughest subjects with ease when you use our learning materials. These lessons and quizzes are all developed by professional instructors, so you can have confidence that you're learning the most accurate information. Our printable lesson transcripts make great offline study guides that outline the most important keywords and topics.
1. The Linear Properties of a Derivative
In this lesson, learn two key properties of derivatives: constant multiples and additions. You will 'divide and conquer' in your approach to calculating the limits used to find derivatives.
2. 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.
3. 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.
4. 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.
5. Differentiating Factored Polynomials: Product Rule and Expansion
Most functions that we want to differentiate are complicated functions for which no single derivative rule will work. In this lesson, learn what happens to derivatives when you multiply functions together.
6. How to Find Derivatives of Implicit Functions
How do you define the rate of change when your function has variables that cannot be separated? Learn how implicit differentiation can be used to find dy/dx even when you don't have y=f(x)!
7. How to Take the Derivative of tan(x)
In this lesson we show how to take the derivative of the tangent function including the cases when the argument is a function of x. As an application, we show how this derivative is used for approximating a function.
8. 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.
9. Finding the Derivative of log(x)
In this lesson, we will learn a formula that we can use to find the derivative of log(x). We'll also look at where this formula comes from and use it to find another well known derivative.
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.
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