Partial Derivative Calculator

This calculator differentiates a polynomial in x, y and z with respect to one variable while the others are held constant. Enter the polynomial, choose the variable, and it returns the partial derivative, the second partial and the full gradient, with the option of evaluating every one of them at a point. A third action prints all four second-order partials and checks that the two mixed partials agree. It handles sums of terms such as 3x^2y - 5xy^3 and nothing else: there is no computer algebra here, so trigonometric, exponential, logarithmic and rational terms are refused rather than guessed at.