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Showing content from https://numpy.org/doc/stable/reference/generated/numpy.polyder.html below:

numpy.polyder — NumPy v2.3 Manual

numpy.polyder(p, m=1)[source]#

Return the derivative of the specified order of a polynomial.

Note

This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.

Parameters:

ppoly1d or sequence

Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see poly1d.

mint, optional

Order of differentiation (default: 1)

Returns:

derpoly1d

A new polynomial representing the derivative.

See also

polyint

Anti-derivative of a polynomial.

poly1d

Class for one-dimensional polynomials.

Examples

The derivative of the polynomial \(x^3 + x^2 + x^1 + 1\) is:

>>> p = np.poly1d([1,1,1,1])
>>> p2 = np.polyder(p)
>>> p2
poly1d([3, 2, 1])

which evaluates to:

We can verify this, approximating the derivative with (f(x + h) - f(x))/h:

>>> (p(2. + 0.001) - p(2.)) / 0.001
17.007000999997857

The fourth-order derivative of a 3rd-order polynomial is zero:

>>> np.polyder(p, 2)
poly1d([6, 2])
>>> np.polyder(p, 3)
poly1d([6])
>>> np.polyder(p, 4)
poly1d([0])

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