# Knowledge Base

## Solution 29110: Finding a Numeric Derivative of a List of Data with Respect to Another List of Data Using the TI-Nspire™ Family Products.

### How can I find a numerical derivative of data, as opposed to a function, using the TI-Nspire family products?

The Vernier DataQuest application has the ability to determine a numeric derivative of a list of data with respect to another list of data. The data can be collected using sensors, input manually, or linked from other applications. The numerical derivative is found using a calculated column (Data > New Calculated Column)

To determine the numerical 1st derivative of List B with respect to List A, enter the following expression in the Column Options dialog:

derivative(B,A,1,0) or derivative(B,A,1,1)

To determine the numerical 2nd derivative of List B with respect to List A, enter the following express:

derivative(B,A,2,0) or derivative (B,A,2,1)

The last parameter is either 0 or 1 depending on the method you are using. When it is 0, a weighted average is used. When it is 1, a time shifted derivative method is used.

Higher order derivatives can be found by applying a derivative calculation to a calculated column that was defined as a derivative. For example , to find the numerical 4th derivative of List B with respect to List A do the following:

Define a calculated column C to be the 2nd derivative of List B with respect to List A [derivative(B,A,2,0) or derivative (B,A,2,1)], then create a new calculated column to be the 2nd derivative of Calculated Column C with respect to List A [derivative(C,A,2,0) or derivative (C,A,2,1).

NOTE: The first derivative calculation (weighted average) is what the Tangent tool uses to display the slope at a data point when examining data. (Analyze > Tangent).

Note: The derivative calculation is completely row based. It is recommended that your List A data be sorted in ascending order.