56 Part I: The Questions
384. f x
x
x
x
x
( )
ln
= −
+ +
+
+
(
)
2
2
1
1
385. f x
x
x
( ) =
( )
+
(
)
log 5
2
3
1
Logarithmic Differentiation
to Find the Derivative
386–389 Use logarithmic differentiation to find the
derivative.
386. f x x
x
( )
tan
=
387. f x
x
x
( ) ln
cos
= ( )
388. f x
x
x
( ) =
−
+
2
2
4
4
389. f x
x
x
x
x
( )
(
)sin
(
)
/
=
−
+
+
1
2
4
3 2
Derivatives Involving
Logarithmic Functions
377–385 Find the derivative of the given function.
377. f
 
(x) = ln (x)
2
378. f
 
(x) = (ln x)
4
379. f x
x
( ) ln
=
+
2
5
380. f x
x
x
( ) log
=
+
+
(
)
10
2
6
381. f x
x
x
( ) log
sin
sin
=
− +
+
6
1 2
4 3
382. f x
x
( ) log log
=
(
)
7
8
5
383. f x
x
x
( ) ln sec
tan
=
+