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20. Using the general property
d
dx
exp(
bx
)=
b
exp(
bx
), we write
v
=
dx
dt
=
µ
d
(19
t
)
dt
¶
·
e
−
t
+(19
t
)
·
µ
de
−
t
dt
¶
.
If a concern develops about the appearance of an argument of the exponential (
−
t
) apparently having
units, then an explicit factor of 1
/T
where
T
= 1 second can be inserted and carried through the
computation (which does not change our answer). The result of this diFerentiation is

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