Commuting 36 kms, 5 days a week
If you are feeling physically worn out by the commute and you are not used to, well, you are just tiring yourself out and not allowing you muscles to recover between rides. 

Keep riding and your body will eventually adapt. Maybe you want to do this commute every other day for a while, or at a slower pace to help you your body strengthen itself.

Simply riding will build strength and endurance. Doing some body weight core exercises will probably help stabilize you torso and let your legs work efficiently.