How
Contents
How#
Calculate the derivative of an expression.#
We can calculate the derivative of an expression using sympy.diff which takes,
an expression, a variable and a degree.
Tip
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.#
We can calculate the indefinite integral of an expression using
sympy.integrate. Which takes an expression and a variable.
Tip
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.#
We 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 we pass a tuple with the variable and the upper
and lower bounds of integration.
Tip
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:
Tip
sympy.oo
For example:
sym.oo
Calculate limits#
We can calculate limits using sympy.limit. The first argument is the
expression, then the variable and finally the expression the variable tends to.
Tip
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)