# numpy.polyder

numpy.polyder(p, m=1)

  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:
    p poly1d or sequence

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

    m int, optional

      Order of differentiation (default: 1)

  Returns:
    der poly1d

      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:

      >>> p2(2.)
      17.0

  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])