# numpy.polynomial.polynomial.polyder

polynomial.polynomial.polyder(c, m=1, scl=1, axis=0)

  Differentiate a polynomial.

  Returns the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the polynomial `1 + 2*x + 3*x**2` while [[1,2],[1,2]] represents `1 + 1*x + 2*y + 2*x*y` if axis=0 is `x` and axis=1 is `y`.

  Parameters:
    c array_like

      Array of polynomial coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.

    m int, optional

      Number of derivatives taken, must be non-negative. (Default: 1)

    scl scalar, optional

      Each differentiation is multiplied by scl. The end result is multiplication by `scl**m`. This is for use in a linear change of variable. (Default: 1)

    axis int, optional

      Axis over which the derivative is taken. (Default: 0).

      New in version 1.7.0.

  Returns:
    der ndarray

      Polynomial coefficients of the derivative.

  See also

  `polyint`

  Examples

      >>> from numpy.polynomial import polynomial as P
      >>> c = (1,2,3,4) # 1 + 2x + 3x**2 + 4x**3
      >>> P.polyder(c) # (d/dx)(c) = 2 + 6x + 12x**2
      array([  2.,   6.,  12.])
      >>> P.polyder(c,3) # (d**3/dx**3)(c) = 24
      array([24.])
      >>> P.polyder(c,scl=-1) # (d/d(-x))(c) = -2 - 6x - 12x**2
      array([ -2.,  -6., -12.])
      >>> P.polyder(c,2,-1) # (d**2/d(-x)**2)(c) = 6 + 24x
      array([  6.,  24.])