def function_and_derivative_trace(list_of_terms, x_values, delta_x):
    traced_function = function_values_trace(list_of_terms, x_values)
    traced_derivative = derivative_values_trace(list_of_terms, x_values, delta_x)
    return make_subplots([traced_function], [traced_derivative])
def function_and_derivative_trace(list_of_terms, x_values, delta_x):
    traced_function = function_values_trace(list_of_terms, x_values)
    traced_derivative = derivative_values_trace(list_of_terms, x_values,
                                                delta_x)
    return make_subplots([traced_function], [traced_derivative])
def side_by_side_derivative_rules(list_of_terms, x_values):
    function_trace = function_values_trace(list_of_terms, x_values)
    derivative_trace = derivative_function_trace(list_of_terms, x_values)
    if derivative_trace and function_trace:
        return make_subplots([function_trace], [derivative_trace])