In that scene, kakashi said something to the effect that he wasn't as strong as he used to be. Then, you could see the struggling in his eye, right after that, you could his fingers slipping from the rocks. Right after that, he closed his eyes and the scene changed to show the chakra circulatory system with all of the gates (or should I say points). Zoomed into one of them (it was in his head where the brain would be) and the they showed it dissapear. Right after that, kakashi made the final climb. Not only did he make it, he made so easily that he pretty much propelled himself with that one arm he had nearly lost all strenght in. After hearing the description of what the opening of the first gate does (releases the limit the brain puts upon how much muscle power you can access) it seemed pretty clear that he opened the first gate. They didn't have to say anything because we had already gotten an explanation of it a few episodes earlier. Kind of like how they don't bother explaining how to mold chakra anymore.

Don't feel sorry for Rock and Gai, because I'd bet my last dollar that their bodies are far stronger than kakashi's, so they can probably make better use of the technique than kakashi can

Edit to Jesper:
I don't think he knew how to do it before he saw rock do it. There had to be a reason he unveiled his eye during the exam and I think it was to copy the technique. I don't think it was just to look and see inside, because I don't think the sharingan can do that, like the byakugan can. If his eye can't do that, and he already knows the technique, then there was no point at all. I'd like to think there was a point.