# Differentiate a polynomial, set the derivatives and multiply each differentiation by a scalar in Python

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To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy. Return the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the polynomial 1 + 2*x + 3*x**2 while [[1,2],[1,2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.

The method returns the Polynomial coefficients of the derivative. The 1st parameter, c is an array of polynomial coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.

The 2nd parameter, m are number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter is scl. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter is axis. It's the axis over which the derivative is taken. (Default: 0).

## Steps

At first, import the required libraries −

import numpy as np
from numpy.polynomial import polynomial as P

Create an array of polynomial coefficients i.e. 1 + 2x + 3x**2 + 4x**3 −

c = np.array([1,2,3,4])


Display the coefficient array −

print("Our coefficient Array...\n",c)

Check the Dimensions −

print("\nDimensions of our Array...\n",c.ndim)


Get the Datatype −

print("\nDatatype of our Array object...\n",c.dtype)

Get the Shape −

print("\nShape of our Array object...\n",c.shape)


To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy −

print("\nResult...\n",P.polyder(c, 2, scl = -1))

## Example

import numpy as np
from numpy.polynomial import polynomial as P

# Create an array of polynomial coefficients i.e.

# 1 + 2x + 3x**2 + 4x**3
c = np.array([1,2,3,4])

# Display the coefficient array
print("Our coefficient Array...\n",c)

# Check the Dimensions
print("\nDimensions of our Array...\n",c.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",c.dtype)

# Get the Shape
print("\nShape of our Array object...\n",c.shape)

# To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy.
print("\nResult...\n",P.polyder(c, 2, scl = -1))

## Output

Our coefficient Array...
[1 2 3 4]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(4,)

Result...
[ 6. 24.]
Updated on 28-Feb-2022 10:36:41