You are asking about the "Trinitarians" view, not about a certain denomination. Because there are many different Trinitarian denominations, various different answers to your question exist.
God can't die, therefore Jesus isn't God.
Jesus dying ... and God ... dying
In my youth I heard about various books written by Christian theologians arguing more or less this way:
"One reason why God became a man is that he wanted to die because he wanted to make the experience of dying."
These authors deny the premise ("God can't die") of the non-Trinitarian's statement (see the second part of my answer).
I don't know which denominations were represented by these theologians, however, it is clear that the statement implies that those denominations at least assume that Jesus is God.
First of all, does the Bible even say that God can't die (I assume it does, or at least it implies it).
You have to be very careful here:
If you assume that there is no life after death, the sentence "some person died" is equivalent to the sentence "the person does not live any more".
However, the Bible assumes that there is a life after death. And if a religion (not necessarily Christianity) assumes that there is a life after death, the sentence "the person died" does not imply that the person does not live any more. The statement that somebody has died does not even imply that the person is dead (even not for a short moment) after having died.
And in reverse, the statement that some person will live forever does not imply that the person does not die.
Unfortunately, I cannot tell you if there is some text in the Bible explicitly saying that God cannot die.
However, the quotes from the Bible given in the other answer only say that God will live forever; assuming that there is a life after death, this does not imply that God cannot die.