In X-Men: First Class, we never see if Darwin actually died.
Did Darwin die or did he survive somehow?
Darwin died, as shown in the movie Shaw forced energy into Darwin's body. From the movie we can assume Darwin can adapt to physical stimuli but at no point do we see any proof he could adapt to energy based stimuli.
So what we see is a attempt by Darwin to adapt that he realizes is fruitless and accepts his death.
In the comics, he is shown to be more resilient and adaptable under similar situations.
After the X-Men hurled Krakoa into space, unaware of the two survivors, Darwin instinctively converted himself into pure energy and bonded with Kid Vulcan, trying to keep them both alive.
Years later, the reality-altering "M-Day" event revived Kid Vulcan. Darwin's consciousness also reawakened inside Vulcan, but he was helpless to prevent Vulcan's vengeful attacks on the X-Men. Telepathically liberated by Rachel Summers, during the conflict, Darwin regained physical form as his mutation quickly rebuilt his body. After recuperating at Xavier's Institute, Darwin agreed to help Xavier locate Vulcan, who had left Earth bound for the interstellar Shi'ar Empire of his birth.
Therefore, though not canon until they address it in the movies, it appears that Darwin was more than able to adapt to the circumstances, and I'd posit that he converted to pure energy, which would explain the explosion.
In the comics he's also shown to turn into pure energy and reform elsewhere when there is no other option, but if memory serves it took him a long time to reform from that, so I say that he definitely survived. it's stated more than once that he can't even die from ageing, the vacuum of space, or being incinerated in a star, so yea, he's still around, just lost and reforming somewhere :P
Darwin has the power of "reactive evolution"; i.e., his body automatically adapts to any situation or environment he is placed in, allowing him to survive possibly anything; the exact nature and limits of his powers have not been revealed. Darwin was shown to be killed very easily by Shaw, by putting energy that Shaw caught in mid air and made it into a ball of energy, Darwin of course turned to metal but gave up and instead turned to some rock and turned into dust.
Now is he really dead? No, his evolution adapting to his environment, as a plant grows from soil so will he from the ground building himself.
From the comics: he fought Hulk but teleported away after being smashed a lot, saying he couldn't absorb enough radiation.
From the movie: he turned into rock when beaten by Havok, he gained gills when submerged in water, he could go toe to toe with any mutant except mind controlled, Leach and Rogue.
He is a survivor of mutants.