Mbappe left Paris St Germain in the close season as the French club's all-time top scorer but his move to Real has been plagued by teething problems, while a hamstring injury and a thigh issue have also hampered his settling-in time.
However, since missing his second penalty in a week in a 2-1 loss at Bilbao Mbappe has scored four goals in all competitions, including the opener in Sunday's 4-2 LaLiga win over Sevilla.
"I took a lot of positives from the Bilbao game. I hit rock bottom," he told Real Madrid TV. "I missed a penalty and I realised at that moment I have to give my all for this shirt and play with personality."
Mbappe now has 10 goals in 16 league appearances, helping Real end the calendar year second in the table, just a point behind leaders Atletico Madrid.
--Reuters--