gCalcD: Calculating Derivatives

To calculate the first derivative, second derivative and some higher order derivatives press the f'(x), f''(x),... button. The first few derivatives of the function are displayed on a new window. To calculate other higher derivatives press Calculate next order derivative.

The derivative calculator instantly recognizes if a function is constant in which case it will return 0. For example, if you type in sin(x)^2+ cos(x)^2, you will get 0 for the function is identically 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)

Press Graph f, f' or Graph f, f', f'' to draw the graphs of the function and its first and/or second derivatives. You will notice wherever the graph of the function f(x) is increasing f'(x) is positive and its graph lies above the x-axis on the related interval; and wherever the graph of f(x) is decreasing f'(x) is negative and its graph lies below the x-axis on the related interval (if the axes are not rotated). Also you will notice wherever the function f(x) is concave-up f''(x) is positive and its graph lies above the x-axis on the related interval; and wherever the function f(x) is concave-down f''(x) is negative and its graph lies below the x-axis on the related interval.

gCalcD can also calculate the derivatives of (functions representing) parametric curves. That is, for p(t) = (x(t), y(t)) you will get p'(t) = (x'(t), y'(t)) when you press the p'(t), p''(t), ... button.