My baby 6 month old has cough week ago and still it is productive cough with no symptoms he eat well and happy i do not see any sputum i just hear it?

Baby with cough: If cough does continue more than a few days longer then you should call your pediatrician to have your baby checked.

6 months old : With productive cough should not be a concern unless your baby is not eating nor drinking. It is good your baby is coughing it up - the mucus. Consult with your pediatrician if your baby developed fever, labored breathing , retracting, wheezing , fussy , restless and cough had worsened

Sick baby: Your baby is probably fine, but if you have any significant questions about its health the best thing to do would be to have them seen by a pediatrician. Always better safe than sorry.