Multivariate Calculus

MVCs are an integral part of mathematics and they can be easily calculated with the sympy module in python.

Calculating partial derivatives

Partial derivatives can be calculated with the sympy.diff(f, x) function. The function will differentiate the function f once with respect to x.

To take multiple derivatives, pass the variable as many times as you wish to differentiate.

For instance, if we were to derive f with respect to x and then to y we would write sympy.diff(f, x, y).

Let’s illustrate this by calculating $\frac{\partial (xy^3+x^2y^2)}{\partial x \partial y}$

import sympy

sympy.diff(x*y**3+x**2*y**2, x, y)