BrownMath.com → TI-83/84/89 → Derivatives
Updated 5 Jan 2014

# Derivatives on 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 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.

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`] [`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.

## 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. 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`].