Devarim (Deut.) ch. 16).. lists the 3 pilgrimage holidays, Pesach, Shavuot and Succot. Of the 3 holidays, Pesach has no explicit mention of "simcha" (joy). Why is that? Is simcha not required on Pesach as with the other holidays? If it is required, is it only Midrabbanan (Rabbinical)?
Yalkut Shimoni in Parshas Emor (654) addresses this: "You won't find even a single mention of simcha by Pesach. Why? Because on Pesach the grain is judged...alternatively, because on Pesach the Egyptians died." The Tanya Rabasi (57) cites the latter explanation, then adds,"...therefore 2 simchos are written by Succos - one for itself [Succos] and one for Pesach."
Tosfos (Chagigah 8a - the last one) writes that the simcha of Pesach is learned through a hekesh from Shvuos.
The Yeraim (127) writes that we learn it from a gzeirah shava from Succos, or from "vsumachta bchagecha" which implies that any holiday on which there is a mitzvah of chagigah, there is a also a mitzvah of simcha.
So it would seem that it's not only Midrabbanan.
The Tzror Hamor says that when am yisroel came out of Egypt on pesach, the torah had not yet been given to them, so that the torah does not mention simcha. in addition to that, they did not know at that time that the mitzrim had been drown until the 7th day of their departure, and it was only at this moment that they rejoiced.
It's written, I believe, but don't know where, that women are exempt from coming 3 times a year to the Beis Hamikdash, because only males are commanded, but they still have to go to Yerushalayim because of the Mitzva of Simchas Yom Tov. Which implies that there is a Mitzva of Simcha of all Sholosh Regolim. Since I don't know the source I can't check the accuracy of this.