# Graphs of Higher Order Derivative Functions

- Author:
- Dr. Jack L. Jackson II

- Topic:
- Calculus, Derivative, Differential Calculus, Functions

## Higher Order Derivative Functions

In the app type in a formula for the original function

*f*(*x*) in the input box. From the shape of the graph can you determine what the shape of the derivative function should look like? Check the checkbox for First Derivative to see its graph. Was it like you expected? Either use the definition of the derivative directly or us derivative shortcut formulas to determine a formula for this first derivative function. Check your work by checking the checkbox for Formulas. The derivative function is itself a function, so it has its own derivative function. This is the second derivative of the original function. What can you say about the shape of the graph of the second derivative by looking at the graph of the original function? What else can you say about the graph of the second derivative by looking at the graph of the first derivative? Once again apply the definition of the derivative or derivative shortcut rules to determine a formula for the second derivative and check it against the provided formula. In a similar manner we can produce higher order derivatives. This app allows you to see the graphs and formulas for up to the fifth derivative.