When you differentiate a function you produce a new function called the Derivative. Performing the same process on this new function gives you "The Second Derivative". Do it again and you have the "Third Derivative". This process of repeating the differentiation process yields what is called "Higher Order Derivatives".
These new functions have important mathematical and practical implications as you will see later. For now, you will learn how to take higher order derivatives in LiveMath and observe their graphs.
First, a word on notation; Most calculus texts will denote successive derivatives with notation similar to the list below:
In LiveMath you take successive derivatives by activating more than one Op and multiplying it onto the old one. The following example will help you with these methods.
Example
3.14 Higher Order Derivatives
NOTE: It is important you input the second derivative correctly. To do this, click on the Derivative Op on the Pallette TWICE. Then type a y, tab and type an x and then tab and type another x.
You want your Op to look like the following:
Not like this, which is the derivative squared.
The third derivative would look like this:
Now you will look at higher order derivatives by using Graph Theories.
Example
3.15 Higher Order Derivatives - by Graphing
This method links all three plots to the original equation. Any changes you make to the originial function will ripple through the Graph Theory. Note: in some cases, changing the function may require you to adjust the viewport. Click on the link below to see this example in action.
LiveMath Internet: Higher Order
Derivatives
