Basic rules: Derivative of x: D[x] = 1 Constant multiple: D[2x] = 2 Exponential: D[e^{x}] = e^{x} Cosine: D[cos x] = -sin x |
Multiple steps: Product Rule: D[x cos x] (two steps) Power Rule: D[(cos x)^{3}] (two steps) Chain Rule: D[cos(x^{2})] (two steps) |
The button next to the "Variable" label displays a pop-up menu which can be used to select a variable for partial derivatives. The selected variable is displayed inside the button. With a variable selected, the "Apply" button applies the derivative operator with respect to the selected variable (e.g. with "y" selected, the operator "Dy[...]" is applied). With no variable selected (the default setting), the standard operator "D[...]" is applied -- this operator is equivalent to "Dx[...]". The pop-up menu shows all available free variables.
The applet can also compute multiple derivatives -- for example, D[D[cos x]] (the second derivative of cos x), which requires three steps to complete.