pip install sympy

# Importing library
import sympy as sym
 
# Declaring variables
x, y, z = sym.symbols('x y z')
 
# expression of which we have to find derivative
exp = x**3 * y + y**3 + z
 
# Differentiating exp with respect to x
derivative1_x = sym.diff(exp, x)
print('derivative w.r.t x: ',
      derivative1_x)
 
# Differentiating exp with respect to y
derivative1_y = sym.diff(exp, y)
print('derivative w.r.t y: ',
      derivative1_y)

derivative w.r.t x:  3*x**2*y
derivative w.r.t y:  x**3 + 3*y**2

# Finding second derivative
# of exp with respect to x
derivative2_x = sym.diff(exp, x, 2)
print('second derivative w.r.t. x: ',
      derivative2_x)
 
# Finding second derivative
# of exp with respect to y
derivative2_y = sym.diff(exp, y, 2)
print('second derivative w.r.t. y: ',
      derivative2_y)

second derivative w.r.t. x:  6*x*y
second derivative w.r.t. y:  6*y

# Indefinite integration of cos(x) w.r.t. dx
integral1 = sym.integrate(sym.cos(x), x)
print('indefinite integral of cos(x): ',
      integral1)
 
# definite integration of cos(x) w.r.t. dx between -1 to 1
integral2 = sym.integrate(sym.cos(x), (x, -1, 1))
print('definite integral of cos(x) between -1 to 1: ',
      integral2)
 
# definite integration of exp(-x) w.r.t. dx between 0 to ∞
integral3 = sym.integrate(sym.exp(-x), (x, 0, sym.oo))
print('definite integral of exp(-x) between 0 to ∞: ',
      integral3)

indefinite integral of cos(x):  sin(x)
definite integral of cos(x) between -1 to 1:  2*sin(1)
definite integral of exp(-x) between 0 to ∞:  1

# Calculating limit of f(x) = x as x->∞
limit1 = sym.limit(x, x, sym.oo)
print(limit1)
 
# Calculating limit of f(x) = 1/x as x->∞
limit2 = sym.limit(1/x, x, sym.oo)
print(limit2)
 
# Calculating limit of f(x) = sin(x)/x as x->0
limit3 = sym.limit(sym.sin(x)/x, x, 0)
print(limit3)

oo
0
1

# assign series
series1 = sym.series(sym.cos(x), x)
print(series1)
 
# assign series
series2 = sym.series(1/sym.cos(x), x, 0, 4)
print(series2)

1 - x**2/2 + x**4/24 + O(x**6)
1 + x**2/2 + O(x**4)