Derivatives on TI83/84
Copyright © 2001–2023 by Stan Brown, BrownMath.com
Copyright © 2001–2023 by Stan Brown, BrownMath.com
Summary: Your TI83 or TI84 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 TI83/84 is helpful in checking your work, but first you must always find the derivative by calculus methods. (See your calculus text.) The TI83/84 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 TI83/84 tell us f′(6), which is the derivative of that function at the point where x = 6?
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 ] [x² ] [+ ] 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. 
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.

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 ]. 
Updates and new info: https://BrownMath.com/ti83/