To calculate the first and second order derivatives of the highlighted function or parametric equation press the Derivative button. The calculated derivatives will be displayed. You can then press Graph f, f' or Graph f, f', f" (or Graph p, p' or Graph p, p', p" in parametric case) to graph the expression together with its first and/or second derivative(s). The Derivative Graphing Calculator inserts he expressions for the derivatives below the highlighted expression or adds to the top of input panel on the left of the calculator.
The derivative calculator instantly recognizes if a function is constant in which case it will return 0. For example, if you calculate the derivative of sin(x)^2+ cos(x)^2 you will get 0 for the function is constant (=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)