numpy.polyder — NumPy v2.2 Manual (original) (raw)

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 thetransition 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])