# Differentiate a polynomial and set the derivatives in Python-NumPy

• Last Updated : 03 Jun, 2022

In this article, we will cover how to differentiate a polynomial and set the derivatives in Python.

## numpy.polynomial.polynomial.polyder method

The Numpy library provides the numpy.polynomial.polynomial.polyder() method to differentiate a polynomial and set the derivatives. The polynomial coefficients c differentiated m times along the axis. The result is multiplied by scl at each iteration (the scaling factor is used for a linear change of variable). The argument c is an array of coefficients ranging from low to high degree along each axis. For example, [5,6,7] represents the polynomial 5 + 6*x + 7*x**2, whereas [[5,6],[5,6]] represents 5 + 5*x + 6*y + 6*x*y if axis=0 is x and axis=1 is y.

Syntax: polynomial.polynomial.polyder(c, m=1, scl=1, axis=0)

Parameters:

• c: array like object.A collection of polynomial coefficients. I
• m: (optional) The number of derivatives taken must not be negative. Standard value is 1.
• scl: (optional) Each differentiation is multiplied by scl. The end result is multiplication by scl**m.. Standard value is 1.
• axis: (optional), int. The axis along which the derivative is computed. The default is 0. If it’s along the columns axis should be set to 1.

Returns: Polynomial coefficients of the derivative.

### Example 1:

In this example, the NumPy package is imported and an array is created which represents the coefficients of a polynomial. numpy.polynomial.polynomial.polyder() is used to differentiate a polynomial and set the derivatives. The shape, datatype and dimension of the array are found by using the .shape, .dtype and .ndim attributes.

## Python3

 `import` `numpy as np``from` `numpy.polynomial ``import` `polynomial as P`` ` `# Creating an array of polynomial coefficients``c ``=` `np.array([``5``,``6``,``7``,``8``])``print``(c)``# shape of the array is``print``(``"Shape of the array is : "``,c.shape)`` ` `# dimension of the array``print``(``"The dimension of the array is : "``,c.ndim)`` ` `# Datatype of the array``print``(``"Datatype of our Array is : "``,c.dtype)`` ` ` ` `# To differentiate a polynomial.``print``(P.polyder(c, ``3``))`

Output:

```[5 6 7 8]
Shape of the array is :  (4,)
The dimension of the array is :  1
Datatype of our Array is :  int64
[48.]```

### Example 2:

In this example derivative of the polynomial is found along the columns axis as set to ‘1’.

## Python3

 `# import packages``import` `numpy as np``from` `numpy.polynomial ``import` `polynomial as P`` ` `# Creating an array of polynomial coefficients``array ``=` `np.array([[``5``,``6``,``7``]])``print``(array)`` ` `# shape of the array is``print``(``"Shape of the array is : "``,array.shape)`` ` `# dimension of the array``print``(``"The dimension of the array is : "``,array.ndim)`` ` `# Datatype of the array``print``(``"Datatype of our Array is : "``,array.dtype)`` ` `# differentiating the polynomial along columns``print``(P.polyder(array,m``=``2``,axis``=``1``))`

Output:

```[[5 6 7]]
Shape of the array is :  (1, 3)
The dimension of the array is :  2
Datatype of our Array is :  int64
[[14.]]```

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