How to Do Derivatives on the TI-89 Titanium

If you want to know how to do derivatives on the TI-89 Titanium, the good news is that one command covers almost everything: d(. The details that trip people up are the order argument, partial derivatives with several letters, implicit curves and getting a slope at a specific point.

The d( command: where it is and what it takes

d( is the 2nd function of the 8 key, and item 1 in the F3 Calc menu. The syntax is d(expression, variable). An optional third argument sets the order, so d(f, x, 2) is the second derivative and d(f, x, 3) the third. Command page: d(.

2nd8→ d(

Work on the HOME screen with Angle set to RADIAN in MODE, because derivatives of sin, cos and tan assume radians. Then type the expression, a comma and the variable, close the parenthesis and press ENTER.

Derivative examples on the TI-89 Titanium and in Calc89
Input	Result
d(x^3,x)	3·x²
d(x·sin(x),x)	x·cos(x)+sin(x)

The second row applies the product rule without any help from you. Chain rule and quotient rule work the same way, and the result comes back simplified. If you want it in a different form, wrap it in expand( or factor( from the F2 Algebra menu.

Derivatives as functions: Define and reuse

When a problem asks for f, f′ and f″ several times, define the function once with Define (F4, item 1). Define f(x)=x^3-3x stores it, and d(f(x),x) differentiates it by name. You can even define the derivative as a new function: Define g(x)=d(f(x),x), then call g(2) like any other function.

F4then1→ Define

The slope at a point: the with operator |

To evaluate a derivative at x = 2, append the with operator and the value: d(x^3,x)|x=2. The | key sits left of the 7 key. The CAS differentiates first, then substitutes, so you never have to store 2 in x. A stored x is the most common reason for derivatives that come out as plain numbers when you expected a formula.

|→ | (with)

For a quick numeric check there is nDeriv(, which uses a difference quotient and returns a decimal. Open F3 and scroll down to it.

F3then scroll to nDeriv( and pressENTER

Numeric derivative example
Input	Result
nDeriv(x^3,x)\|x=2	12.0

Putting d(x^3,x)|x=2 next to this row is a good habit: the exact and the numeric slope should agree, and if they do not, look for a typo in the expression.

Partial derivatives on the TI-89

There is no separate command for a TI-89 partial derivative. d( already differentiates with respect to the variable you name and treats every other letter as a constant. So d(x^2·y^3,x) is the partial derivative with respect to x, and d(x^2·y^3,y) the one with respect to y.

Mixed partials: nest the command, d(d(f,x),y).
Second partial in one variable: use the order argument, d(f,x,2).
At a point: add both values with and, d(f,x)|x=1 and y=2.
Times signs: type x·y with the times key. Without it, xy is a single variable name, not a product.

Make sure y and z hold no stored values. If y is 5 from an earlier problem, the CAS substitutes it before differentiating and the partial derivative with respect to y disappears.

Implicit differentiation with impDif(

For a curve like a circle, where y is not solved for x, use impDif(. It takes the equation, the independent variable and the dependent variable, and returns dy/dx. On the handheld you type it from CATALOG or letter by letter; an optional fourth argument gives a higher order.

CATALOGthen scroll to impDif( and pressENTER

Implicit differentiation example
Input	Result
impDif(x^2+y^2=1,x,y)	−x/y

To get the slope at a point on the curve, add both coordinates after the with operator. For related rates problems, the same idea applies: differentiate with respect to t and treat x and y as functions of t.

Tangent lines, normal lines and extrema

On the handheld, the tangent line comes from the graph screen: F5 Math, then Tangent, then pick the point. Calc89 also accepts tangentLine( and normalLine( on the home line, which return the line as an equation in x.

Tangent and normal line examples in Calc89
Input	Result
tangentLine(x^2,x,1)	2·x−1
normalLine(x^2,x,1)	−x/2+3/2

For optimization, the first derivative test is built in. fMin( and fMax( in the F3 menu return the x value where the expression reaches its minimum or maximum. Solving d(f,x)=0 with solve( from F2 gives all critical points instead.

F36→ fMin(

Minimum and maximum examples
Input	Result
fMin(x^2-4x,x)	x=2
fMax(-x^2+2x,x)	x=1

In Calc89

Calc89 is a CAS graphing calculator intended for use with TI-89 Titanium. d( is on 2nd 8, the with operator on the same key as on the handheld, and the F3 menu holds the calculus commands. Every result above comes from a verified example of the Calc89 CAS. To check homework, scan the problem with the camera and Calc89 builds the input. The AI keystroke tutor shows the key sequence for the TI-89 Titanium, so the steps carry over to the handheld you take into the exam. Calc89 is free to download, Pro features as an in-app purchase.

Frequently asked questions

What is the difference between d( and nDeriv(?

d( differentiates symbolically and returns a formula. nDeriv( estimates the slope numerically and returns a decimal at one point.

How do I take a second derivative?

Add the order as a third argument: d(f,x,2). Nesting d(d(f,x),x) gives the same result.

Why does my derivative contain a number instead of x?

x still holds a stored value. Run NewProb from the Clean Up menu (2nd F1) or delete the variable.

Can I use Calc89 on the AP Calculus exam?

No. Phone and tablet apps are not permitted on standardized exams. As of October 2026, AP Calculus AB and BC permit the physical TI-89 Titanium on the calculator sections.

Derivatives on the TI-89 Titanium: d(, Partial and Implicit Differentiation