Howbeit this kind goeth not out but by prayer and fasting.
Note 4 at Mt 17:21: Prayer and fasting do not drive out certain demons. If the name of Jesus and faith in His name won't do the job, fasting and prayer won't either. Jesus was saying that fasting and prayer are the only ways of casting out this type of unbelief.
An unbelief that comes as a result of ignorance can be done away with by receiving the truth of God's Word (Ro 10:17 and 2Pe 1:4). However, the unbelief that hindered the disciples in this case was a "natural" type of unbelief (see note 2 at Mt 17:20). They had been taught all of their lives to believe what their five senses told them. They were simply dominated by this natural input more than by God's supernatural input (God's Word - Lu 9:1). The only way to overcome this unbelief that comes through the senses is to deny the senses through prayer and fasting (see note 1 at Mt 4:2).