Find Derivatives of Parametric Equations with the TI-83 Plus

By C. C. Edwards

You can use the TI-83 Plus graphing calculator to find the derivative (dy/dx, dy/dt, or dx/dt) of a pair of parametric equations at a specified value of T:

  1. Graph the parametric equations in a viewing window that contains the specified value of T.

    If you want to get a viewing window that contains the specified value of T, make sure that value is between Tmin and Tmax.

  2. Set the Format menu to ExprOn and CoordOn.

  3. Press [2nd][TRACE] to access the Calculate menu.

  4. Press [2], [3], or [4] to respectively select the dy/dx, dy/dt, or dx/dt option.

  5. If necessary, repeatedly press


    until the appropriate parametric equations appear at the top of the screen.

  6. Enter the specified value of T.

    To do so, use the keypad to enter the value of T. As you use the keypad, T= replaces the coordinates of the cursor location appearing at the bottom of the screen in the previous step. The number you key in is placed after T=. If you make a mistake when entering your number, press [CLEAR] and re-enter the number.

    If you’re interested only in finding the slope of the curve in a general area of the graph (instead of at a specific value of T), then instead of entering a value of T, just use the




    to move the cursor to the desired location on the graph.

  7. Press [ENTER].

    After pressing [ENTER], the derivative is displayed at the bottom of the screen.