Why is the derivative of 2^x not x*2^(x-1)?

That technique for calculating derivatives only works for polynomial terms, that is terms of the form x^n, where n is some number. Here though our variable x is in the exponent, and so the term is not polynomial but exponential so the method of multiplying by the power and then reducing it by 1 will not work.

To convince yourself that the answer above is incorrect, remember that a derivative represents the instantaneous rate of change of a function. If we consider the graph of 2^x we see that it is always increasing. However, if we evaluated x*2^(x-1) at x = -1, we would get a value of -1/4, indicating that the function is decreasing. So we know this answer cannot possibly be correct. In order to find the correct answer we would need to go back to first principles, where we find that the real derivative is ln2 * 2^x