second, your notation leaves much to be desired. use parentheses to make your expressions clear.
from your work, I assume your function is
f(x) = 2^(x^2+3x) rather than f(x) = 2^(x^2) + 3x
f'(x) = 2^(x^2+3x) * (2x+3) * ln(2)
f'(3) = 2^(18) * (9) *ln(2) ... which, yes, is a very large number.