Guide to Calculating and Graphing Derivatives

Our powerful graphing calculator instantly computes the first- and second-order derivatives of a function or parametric expression currently active (in focus) and can graph them simultaneously.

Calculate, Graph, and Insert Derivatives

• Calculate Derivatives: Press the Derivative button. The derivatives are displayed on the screen, along with options to graph them.
• Graph the Derivatives:
  • To graph the derivative(s) of a function, press the Graph f(x), f'(x) or Graph f(x), f'(x), f"(x) buttons.
  • For a parametric curve, the buttons appear as Graph p(t), p'(t) or Graph p(t), p'(t), p"(t).
• Insert Derivatives to Multi-input Pane: You can also add the calculated derivatives to the multi-input pane by selecting them. They will be appended as highlighted new input panels at the bottom of the pane.
• Press the Done button to close the derivative window.

Notes on Derivatives

The derivative graphing calculator instantly detects if a function is constant in which case it will return 0 as its derivative. For example, entering sin(x)^ 2+ cos(x)^2 yields 0, since the function is constant throughout its domain (always equal to 1).

The form of the derivative calculated may look different from but equivalent to what you might expect. For example, the derivative of: f(x) = sin(x)cos(x) is calculated as: f'(x) = cos(x)*cos(x) + sin(x)*-sin(x) which is equivalent to: f'(x) = cos²(x) - sin²(x)

Importance in Calculus

In calculus, the first and second order derivatives are important for graphing functions and parametric curves.

When you append the panels containing the computed derivatives, you can use them to find, for example, the first- or second-order critical points of the function by pressing the Solve button.

Observations on Graphs