Solution Let y = xsin x Taking logarithm on both sides, we have
log y = sin x log x
Therefore
1 dy
y dx  = sin
(log )
log
(sin )
d
d
x
x
x
x
dx
dx
+
or
1 dy
y dx  =
(sin )1
log
cos
x
x
x
x +
or
dy
dx  =
sin
cos
log
x
y
x
x
x


+




=
sin
sin
cos
log
x
x
x
x
x
x


+




=
sin
1
sin
sin
cos
log
x
x
x
x
x
x
x
− ⋅
+
⋅
Example 30 Find dy
dx , if yx + xy + xx = ab Solution Given that yx + xy + xx = ab