`numpy:polyder`

Signature

def polyder ( p , m = 1 )

Return the derivative of the specified order of a polynomial.

p : poly1d or sequence: Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see poly1d.
m : int, optional: Order of differentiation (default: 1)

The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is:

import numpy as np

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

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which evaluates to:

p2(2.)

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

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

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

np.polyder(p, 2)
np.polyder(p, 3)
np.polyder(p, 4)

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