Python | sympy.Derivative() method

Last Updated : 12 Jul, 2025

With the help of sympy.Derivative() method, we can create an unevaluated derivative of a SymPy expression. It has the same syntax as diff() method. To evaluate an unevaluated derivative, use the doit() method.

Syntax: Derivative(expression, reference variable) Parameters: expression - A SymPy expression whose unevaluated derivative is found. reference variable - Variable with respect to which derivative is found. Returns: Returns an unevaluated derivative of the given expression.

Example #1:

Python3

# import sympy 
from sympy import * 

x, y = symbols('x y')
expr = x**2 + 2 * y + y**3
print("Expression : {}".format(expr))
 
# Use sympy.Derivative() method 
expr_diff = Derivative(expr, x)  
    
print("Derivative of expression with respect to x : {}".format(expr_diff))  
print("Value of the derivative : {}".format(expr_diff.doit()))

Output:

Expression : x**2 + y**3 + 2*y 
Derivative of expression with respect to x : Derivative(x**2 + y**3 + 2*y, x)
Value of the derivative : 2*x

Example #2:

Python3

# import sympy 
from sympy import * 

x, y = symbols('x y')
expr = y**2 * x**2 + 2 * y*x + x**3 * y**3
print("Expression : {}".format(expr))
 
# Use sympy.Derivative() method 
expr_diff = Derivative(expr, x, y)  
    
print("Derivative of expression with respect to x : {}".format(expr_diff))  
print("Value of the derivative : {} ".format(expr_diff.doit()))

Output:

Expression : x**3*y**3 + x**2*y**2 + 2*x*y 
Derivative of expression with respect to x : Derivative(x**3*y**3 + x**2*y**2 + 2*x*y, x, y)
Value of the derivative : 9*x**2*y**2 + 4*x*y + 2

Example #3:

Python3

# import sympy 
from sympy import * 

# Derivative method for trigonometric functions
x, y = symbols('x')
expr = sin(x) + cos(x)
print("Expression : {}".format(expr))

 
# Use sympy.Derivative() method 
expr_diff = Derivative(expr, x)  
    
print("Derivative of expression with respect to x : {}".format(expr_diff))  
print("Value of the derivative : {}".format(expr_diff.doit()))

Output:

Expression : sin(x) + cos(x)
Derivative of expression with respect to x : Derivative(sin(x) + cos(x), x)
Value of the derivative : -sin(x) + cos(x)

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Python | sympy.Derivative() method

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