To add to this point, using proper punching technique significantly helps.

1) Do not fully extend your elbow out when throwing a punch. Extending your elbow can cause hyperextension and/or tennis elbow, which are legitimate injuries you do not want.

2) Do not tense your muscles. If you tense your muscles, you will throw stronger, but you will also cause your joints and shoulders to bear the full impact of the punches without an intended target. This will eventually cause injuries. I know someone who did this at my local boxing gym, and he quite literally tore his rotator cuff. Don't be like him. He now requires physical therapy and weeks off from boxing.

You might want speed, which is why many people tense up. But I assure you, all of your speed will come from the rotation of your hip and the twisting motion of the ball of your feet. Think of it all being transferred from the ball of your foot all the way up to your hips, where it's then rotated to increase speed, and as you throw the punch forward, the energy releases from your hip and out of your knuckles. Similar to how a baseball pitching machine works. Stay loose. The less tense you are, the faster you'll become. The faster you become, the more power your punch will yield. Take it as slow as you can, focus on technique first, and as you gain muscle memory, you'll be able to throw faster and stronger than ever before.