"""Computes the derivative of the inverse Euler ZYX body transformation matrix.

Given Euler angles and angular velocity, this function calculates the derivative of the inverse transformation matrix for the ZYX Euler sequence. The function constructs two intermediate matrices, J_y and J_z, based on the Euler angles and then combines them with the angular velocity to produce the final derivative matrix.

Args:
    euler_coordinates (numpy.ndarray): A 3-element array containing the Euler angles [roll, pitch, yaw] in radians.
    omega (numpy.ndarray): A 3-element array representing the angular velocity in the body frame.

Returns:
    numpy.ndarray: A 3x3 matrix representing the derivative of the inverse Euler ZYX body transformation matrix.
"""
You should write code starting with:
import numpy as np
import math

def S_inv_eulerZYX_body_deriv(euler_coordinates: np.ndarray, omega: np.ndarray) -> np.ndarray:
    # TODO: Implement this function
    pass

