Smooth Mouse-Look

Unity Engine
1

I’ve created a fairly simple mouse-look script for an fps game i’m working on, however I’ve noticed that while the mouse movement appears smooth, whenever I strafe around objects I get this annoying jittery look on objects that I focus on. Can someone take a look at my code, and tell me how I might improve it?

public class PlayerLook : MonoBehaviour
{
    public float mouseSensitivity = 100.0f;
    public float clampAngle = 80.0f;

    private float mouseX;
    private float mouseY;

    private float rotationX = 0.0f;
    private float rotationY = 0.0f;

    void Start()
    {
        Vector3 rotation = transform.localRotation.eulerAngles;
        rotationX = rotation.x;
        rotationY = rotation.y;
    }

    void Update()
    {
        mouseX = Input.GetAxis("Mouse X");
        mouseY = Input.GetAxis("Mouse Y");

        rotationX += mouseY * mouseSensitivity * Time.deltaTime;
        rotationY += mouseX * mouseSensitivity * Time.deltaTime;   

        rotationX = Mathf.Clamp(rotationX, -clampAngle, clampAngle);

        Quaternion localRotation = Quaternion.Euler(rotationX, rotationY, 0.0f);

        transform.rotation = Quaternion.Lerp(transform.rotation, localRotation, Time.fixedTime);
    }
}
2

I think I figured it out, my update functions on my rigidbody player and my mouse-look camera were different from each other. I changed them both to FixedUpdate and now it looks much smoother.