How
Contents
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)
To compute the second derivative: \(\frac{d ^ 2 (4 x ^ 3 + 2 x + 1}{dx ^ 2}\)
sym.diff(expression, x, 2)
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)
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))
Use \(\infty\)#
In sympy we can access \(\infty\) using sym.oo:
Usage
sympy.oo
For example:
sym.oo
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)