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# Differentiate a polynomial and set the derivatives in Python

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). The result is (d**3/dx**3)(c) = 24

## Steps

At first, import the required library −

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. 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 −

print("\nResult...\n",P.polyder(c, 3))

## 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, 3))

## 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... [24.]

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