Since the given function has the form "e raised to a quantity", we use the chain rule:
d
dx
e
u
=
e
u
d
u
dx
d
dx
e
4x
2
2
=
e
4x
2
2
d
dx
[
4x
2
2
]
=
e
4x
2
2
(8x)
222]2222]2