How#

Calculate the derivative of an expression.#

You can calculate the derivative of an expression using sympy.diff which takes, an expression, a variable and a degree.

Usage

sympy.diff(expression, variable, degree=1)

The default value of degree is 1.

For example to compute \(\frac{d (4 x ^ 3 + 2 x + 1}{dx}\):

import sympy as sym

x = sym.Symbol("x")
expression = 4 * x ** 3 + 2 * x + 1
sym.diff(expression, x)
\[\displaystyle 12 x^{2} + 2\]

To compute the second derivative: \(\frac{d ^ 2 (4 x ^ 3 + 2 x + 1}{dx ^ 2}\)

sym.diff(expression, x, 2)
\[\displaystyle 24 x\]

Calculate the indefinite integral of an expression.#

You can calculate the indefinite integral of an expression using sympy.integrate. Which takes an expression and a variable.

Usage

sympy.integrate(expression, variable)

For example to compute \(\int 4x^3 + 2x + 1 dx\):

sym.integrate(expression, x)
\[\displaystyle x^{4} + x^{2} + x\]

Calculate the definite integral of an expression.#

You can calculate the definite integral of an expression using sympy.integrate. The first argument is an expression but instead of passing a variable as the second argument you pass a tuple with the variable as well as the upper and lower bounds of integration.

Usage

sympy.integrate(expression, (variable, lower_bound, upper_bound))

For example to compute \(\int_0^4 4x^3 + 2x + 1 dx\):

sym.integrate(expression, (x, 0, 4))
\[\displaystyle 276\]

Use \(\infty\)#

In sympy we can access \(\infty\) using sym.oo:

Usage

sympy.oo

For example:

sym.oo
\[\displaystyle \infty\]

Calculate limits of an expression#

You can calculate using sympy.limit. The first argument is the expression, then the variable and finally the expression the variable tends to.

Usage

sympy.limit(expression, variable, value)

For example to compute \(\lim_{h \to 0} \frac{4 x ^ 3 + 2 x + 1 - 4(x - h)^3 - 2(x - h) - 1}{h}\):

h = sym.Symbol("h")
expression = (4 * x ** 3 + 2 * x + 1 - 4 * (x - h) ** 3 - 2 * (x - h) - 1) / h
sym.limit(expression, h, 0)
\[\displaystyle 12 x^{2} + 2\]