Finding a numerical derivative on the TI-84 is quite simple. 

Homescreen Method

Graphical Method

It is also possible to graph the derivative of a function on the TI-84 without actually finding the algebraic representation for the derivative.

Graphing a Derivative Function

  Homescreen Method  
Directions Older OS for TI- & TI84 New Operating System for TI-84 Plus (ver. 2.53 and above)
Select Math:8. nDeriv(
This will paste the command line on your homescreen.
Following the parentheses, you need to type the equation for which you want the derivative. 
Follow this with a comma, the variable x (since this is the variable in the function, another comma, and the number at which you want the numerical derivative. Close this command line with a closed parentheses.
Press enter and this command line is executed and the numerical answer is printed on the screen
     

 

Graphical Method

First type in the equation in a function slot for which you want to find the numerical derivative.

Graph the equation in an appropriate window.

Press 2nd CALC and select choice 6:  dy/dx

Use the cursor arrows to move you to the location or simply type in the x value on the screen.

Press ENTER.   The screen indicates that the derivative of this function at x = 1 is 2. 

 

Graphing a Derivative Function
Directions Older OS for TI- & TI84 New Operating System for TI-84 Plus (ver. 2.53 and above)
     
To graph the derivative of a function type the command line shown above for the homescreen method in a function slot.  This command will be slightly different because you will want the calculator to determine the numerical derivative at each point x on the selected window.  Therefore, you end the command line with and x rather than a number. Press ALPHA F2 and select Nderiv(

 

Be sure to select a window that will be able to visualize all the derivative values you will be hoping to see.  Then press GRAPH.  This graph shows the derivative of the original function .