Moving 3rd person camera around car

Hi
I made a simple script that allows the user to move the camera with mouse movement.
It works like a charm, but now I would like to add a starting position(directly behind the car).

Since the car is moving I would need to calculate the mouseX and mouseY positions from the car current position. I have no idea, how I could archive that.
Also, how could I move the camera, when the car is rotating?

Camera mouse movement script:

        mouseX -= Input.GetAxis("Mouse Y") * sensitivity;
        mouseY += Input.GetAxis("Mouse X") * sensitivity;
        mouseX = Mathf.Clamp(mouseX, minMaxXAngle[0], minMaxXAngle[1]);

        Vector3 targetR = new Vector3(mouseX, mouseY);

        transform.eulerAngles = targetR;

        transform.position = target.position - transform.forward * distanceDamp;        
        
        //Debug.Log(target.transform.rotation.x + "         " + target.transform.rotation.x);    

        Vector3 temp = transform.position;
        temp.y += 1;

Try making the camera a child of the car. Then you wont have to worry about calculating the new position of the camera.