code: def backward(self, indexes, grads):
      (x,) = self.get_retained_inputs()
      (y,) = self.get_retained_outputs()
      (gy,) = grads
  
      if self.axis is not None:
          actual_axis = []
          for axis in self.axis:
              if axis < 0:
                  axis = len(x.shape) + axis
              actual_axis.append(axis)
          for axis in sorted(actual_axis):
              gy = chainer.functions.expand_dims(gy, axis=axis)
              y = chainer.functions.expand_dims(y, axis=axis)
      gy = chainer.functions.broadcast_to(gy, x.shape)
      y = chainer.functions.broadcast_to(y, x.shape)
      gx = gy * chainer.functions.exp(x - y)
      return (gx,)
  
file_path: chainer/chainer/functions/math/logsumexp.py
imports: import six
  import chainer
  from chainer import backend
  from chainer import function_node
  from chainer import utils
  from chainer.utils import type_check
  import chainerx
label_desc: Use image node_id 5 for calling the LogSumExp obj's underlying member method code with example usage: obj.backward(indexes, grads) and returns: gx