Lizard Jew wrote: Deutero-Isaiah?
the second one. how do they think they know its written later?
Because certain parts of Isaiah do not make sense unless they were written after Lehi left Jerusalem which would make it impossible to already have been written on the plates of Laben. Here is more information on the subject.
Two anachronisms in the book relate to the issue of Isaiah. First, critical scholars with good reason have concluded that much of the biblical book, especially chapters 40-66, do not come from the eight century BCE prophet Isaiah, but from a later time. For example, the temporal perspective in chapters 40-55 (from which several of the BM Isaiah chapters come) is that of about 540 BCE. The people have recently suffered destruction at the hands of the Babylonians (in 586 BCE). The temple, Jerusalem, and other cities have been destroyed and need rebuilding. Many of the people are now in Mesopotamia, in captivity; but Babylonian might is waning and release from captivity is imminent. Cyrus, the Persian king, is the political leader who will effect the release (c. 538 BCE). It is not just the mention of specific sixth-centry BCE historical figures and events that pin these chapters to that time. Also telling is that precision in description ceases at this point in time. The era after the release is described in general terms, and this description is in error since bounteous blessing did not ensue. The lack of fulfillment gave Jewish, Christian and Mormon interpreters cause to reapply the chapters to later events. That Isaiah 40-55 were written after the middle of the sixth century BCE is also indicated by their perfect conceptual fit between other prophetic works written in the first half of the sixth century BCE (Jeremiah and Ezekiel) and those written at the end of this century (Haggai and Zechariah 1-8). This dating for this part of Isaiah means it could not have been available to Lehi's family when they, according to the story, left for the New World around 600 BCE--Nephi, Jacob, Abinadi, and Noah's false priests could not have cited from it.
The second anachronism is the BM's interpretation of Isaiah. This, which generally follows cited portions of Isaiah (cf. 1 Ne 22; 2 Ne 9-10, 25-33; Mos 12:25-31; 3 Ne 23:1-5) though is sometimes interspersed within the citiation (cf. 2 Ne 6:6-18; 26:15-27:35), for the most part reinterprets the Isaiah passages to apply to the time of Joseph Smith and the course of Jewish and Christian history up to his time. This reflects the compositional horizon of the book, just as various passages in Second Isaiah (noted above) reflect that work's compositional horizon. Indeed, the course of history laid out in the interpretation and elsewhere in the BM is clear and defined up to the time of the appearance of the BM, but is quite unspecific about events thereafter, just as Second Isaiah is quite indefinite about events after about 540 BCE. Furthermore, the BM shares perceptions about the meaning of Isaiah and methods of prophetic interpretation that were extant among students and readers of Isaiah in the decades just before the BM came forth. This chronological horizon and these interpretive views are evidence that the interpretation of Isaiah in the BM is the work of Smith himself.