code: def 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
         :doc:`transition guide </reference/routines.polynomials>`.
  
      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 :math:`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])
  
      """
      m = int(m)
      if m < 0:
          raise ValueError(
              "Order of derivative must be positive (see polyint)"
          )
  
      truepoly = isinstance(p, poly1d)
      p = NX.asarray(p)
      n = len(p) - 1
      y = p[:-1] * NX.arange(n, 0, -1)
      if m == 0:
          val = p
      else:
          val = polyder(y, m - 1)
      if truepoly:
          val = poly1d(val)
      return val
  
imports: import functools
  import re
  import warnings
  from .._utils import set_module
  import numpy.core.numeric
  from numpy.core import isscalar, abs, finfo, atleast_1d, hstack, dot, array, ones
  from numpy.core import overrides
  from numpy.lib.twodim_base import diag, vander
  from numpy.lib.function_base import trim_zeros
  from numpy.lib.type_check import iscomplex, real, imag, mintypecode
  from numpy.linalg import eigvals, lstsq, inv
label_desc: Use image node_id 8 for calling a global function with example usage: polyder(p, m) and returns: val