Graphing Calculator with Derivatives Graph, Solve, Differentiate
(Partial) Derivative Calculator Calculate derivatives with respect to any variable and partial derivatives
calculator-grapher.com
Graphing Calculator with Derivatives Graph, Solve, Differentiate
(Partial) Derivative Calculator Calculate derivatives with respect to any variable and partial 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.
To calculate the derivative of a one-variable function or partial derivative of a multi-variable function F with respect to a variable, type in the variable in the box provided and press Calculate Derivative.
The derivative will be displayed on a new panel. You can then calculate its derivative, or the derivative of its primitive(s) with respect to any variable by typing in the variable and pressing Calculate Derivative on the relevant panel.
Although you can continue calculating derivatives indefinitely, only < 10 derivative panels will be visible before the shaded area is filled with them. Close any panel by pressing x to make space for newer derivative panels.
The label Fxy means derivative of F with respect to x and then with respect to y.