Derivatives on the TI-83/84

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 section 2.1 of L-H-E Calculus 7e and the lecture notes.) 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.

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

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] [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.
You can get the derivative at other points, if you need to.	Press [2nd] [CALC] [6] again, enter the new x value, and press [ENTER].