t x, we have
1 dy
y dx  = log a
or
dy
dx  = y log a
Thus
(
x)
d
dxa
 = ax log a
Alternatively
(
x)
d
dxa
 =
log
log
(
)
( log )
x
a
x
a
d
d
e
e
x
a
dx
dx
=
= ex log a log a = ax log a Rationalised 2023-24
 MATHEMATICS
132
Example 29 Differentiate xsin x, x > 0 w