polynomial.polynomial.polyder(c, m=1, scl=1, axis=0)[source]#

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.


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.

mint, optional

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

sclscalar, 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)

axisint, optional

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

New in version 1.7.0.


Polynomial coefficients of the derivative.

See also



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