TC3 → Stan Brown → TI-83/84/89 → Derivatives
revised 5 Jan 2014

Derivatives on TI-83/84

Copyright © 2001–2014 by Stan Brown, Oak Road Systems

Summary: Your TI-83 or TI-84 can’t differentiate in symbols, but it can find the derivative at any point by using a numerical process. That can be a big help to you in checking your work, and this page shows you two ways to do it.

The TI-83/84 is helpful in checking your work, but first you must always find the derivative by calculus methods. (See your calculus text.) The TI-83/84 sometimes finds a derivative where none exists (for instance, the derivative of | x | at 0), and if you haven’t found the derivative yourself you may be fooled.

graph of -x squared+9x-14 The function f(x) = −x²+9x−14 is graphed at left. How can the TI-83/84 tell us f′(6), which is the derivative of that function at the point (6,4)?

Method 1: nDeriv

Get to the home screen. Press [2nd MODE makes QUIT].
Paste the nDeriv function. Press [MATH] [] [] [] to select nDeriv. Press [ENTER].
First argument: the function −x²+9x−14 [(-)] [x,T,θ,n] [] [+] 9 [x,T,θ,n] [-] 14
Second argument: the variable name x [,] [x,T,θ,n]
Third argument: the x value where you want the derivative: 6 [,] 6 [)] [ENTER].
The answer −3 appears.

Method 2: Graphing

You can also get the approximate derivative while the graph of the function is displayed.

Graph the function. Press [Y=], make sure no other graphs or plots are highlighted, and enter the function.
 
Press [ZOOM] [6] to start graphing most functions, or [ZOOM] [7] for most trig functions.
The x value where you want the derivative has to be on screen. If necessary, press [WINDOW] and adjust Xmin and Xmax. Then press [GRAPH].
 
If your Xmin and Xmax are right but you don’t see the graph, adjust Ymin and Ymax, or try [ZOOM] [0] to tell the calculator to adjust them.
Select numeric differentiation. [2nd F4 makes CALC] [6] selects dy/dx and redisplays the graph.
 
Enter the desired x value, such as 6. Press [ENTER]. The calculator displays the derivative at the bottom of the screen.
calculated derivative
You can get the derivative at other points, if you need to. Press [2nd F4 makes CALC] [6] again, enter the new x value, and press [ENTER].

This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.

For updates and new info, go to http://www.tc3.edu/instruct/sbrown/ti83/