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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def differentiate(self, coord, edge_order=1, datetime_unit=None):
 """ Differentiate with the second order accurate central differences. .. note:: This feature is limited to simple cartesian geometry, i.e. coord must be one dimensional. Parameters coord: str The coordinate to be used to compute the gradient. edge_order: 1 or 2. Default 1 N-th order accurate differences at the boundaries. datetime_unit: None or any of {'Y', 'M', 'W', 'D', 'h', 'm', 's', 'ms', 'us', 'ns', 'ps', 'fs', 'as'} Unit to compute gradient. Only valid for datetime coordinate. Returns ------- differentiated: Dataset See also -------- numpy.gradient: corresponding numpy function """

        from .variable import Variable

        if coord not in self.variables and coord not in self.dims:
            raise ValueError('Coordinate {} does not exist.'.format(coord))

        coord_var = self[coord].variable
        if coord_var.ndim != 1:
            raise ValueError('Coordinate {} must be 1 dimensional but is {}'
                             ' dimensional'.format(coord, coord_var.ndim))

        dim = coord_var.dims[0]
        if _contains_datetime_like_objects(coord_var):
            if coord_var.dtype.kind in 'mM' and datetime_unit is None:
                datetime_unit, _ = np.datetime_data(coord_var.dtype)
            elif datetime_unit is None:
                datetime_unit = 's'  # Default to seconds for cftime objects
            coord_var = coord_var._to_numeric(datetime_unit=datetime_unit)

        variables = OrderedDict()
        for k, v in self.variables.items():
            if (k in self.data_vars and dim in v.dims and
                    k not in self.coords):
                if _contains_datetime_like_objects(v):
                    v = v._to_numeric(datetime_unit=datetime_unit)
                grad = duck_array_ops.gradient(
                    v.data, coord_var, edge_order=edge_order,
                    axis=v.get_axis_num(dim))
                variables[k] = Variable(v.dims, grad)
            else:
                variables[k] = v
        return self._replace_vars_and_dims(variables)