docstr: Evaluate many derivatives of the polynomial at the point x.
  
  The function produce an array of all derivative values at
  the point x.
  
  Parameters
  ----------
  x : cupy.ndarray
      Point or points at which to evaluate the derivatives
  der : int or None, optional
      How many derivatives to extract; None for all potentially
      nonzero derivatives (that is a number equal to the number
      of points). This number includes the function value as 0th
      derivative
  
  Returns
  -------
  d : cupy.ndarray
      Array with derivatives; d[j] contains the jth derivative.
      Shape of d[j] is determined by replacing the interpolation
      axis in the original array with the shape of x
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code: def derivatives(self, x, der=None):
      """Evaluate many derivatives of the polynomial at the point x.
  
      The function produce an array of all derivative values at
      the point x.
  
      Parameters
      ----------
      x : cupy.ndarray
          Point or points at which to evaluate the derivatives
      der : int or None, optional
          How many derivatives to extract; None for all potentially
          nonzero derivatives (that is a number equal to the number
          of points). This number includes the function value as 0th
          derivative
  
      Returns
      -------
      d : cupy.ndarray
          Array with derivatives; d[j] contains the jth derivative.
          Shape of d[j] is determined by replacing the interpolation
          axis in the original array with the shape of x
  
      """
      x, x_shape = self._prepare_x(x)
      y = self._evaluate_derivatives(x, der)
  
      y = y.reshape((y.shape[0],) + x_shape + self._y_extra_shape)
      if self._y_axis != 0 and x_shape != ():
          nx = len(x_shape)
          ny = len(self._y_extra_shape)
          s = (
              [0]
              + list(range(nx + 1, nx + self._y_axis + 1))
              + list(range(1, nx + 1))
              + list(range(nx + 1 + self._y_axis, nx + ny + 1))
          )
          y = y.transpose(s)
      return y
  
imports: import cupy
  from cupyx.scipy._lib._util import _asarray_validated, float_factorial
label_desc: Use image node_id 1 for calling the _Interpolator1DWithDerivatives obj's underlying member method code with example usage: obj.derivatives(x, der) and returns: y