>>333
lim_[h→0] [e^{(h+1)^2}-e^(h^2+1)]/h
=lim_[h→0] e^(h^2+1)[e^(2h)-1]/h
=lim_[h→0] {2*e^(h^2+1)}{[e^(2h)-1]/(2h)}
=(2*e)*e^0
=2*e

f(x) = e^xとして
lim_[h→0]{[e^(2h)-1]/(2h)}
=lim_[2h→0]{[e^(2h)-e^0]/(2h)}
=f'(0)
=1