53
Chapter 5: The Product, Quotient, and Chain Rules
366. f x
x
x
x
( )
(
)
=
−
+
(
)
1
3
2
5
367. f x
x
x
( ) =
+
−
1
1
, where x > 1
368. f x
x
( ) sin sin sin
=
( )
(
)
(
)
2
369. f x
x
x
( ) =
+
3
370. f x
x
x x
( ) (
)
= +
+ −
(
)
1 5
2
4
2
7
More Challenging Chain Rule
Problems
371–376 Solve the problem related to the chain rule.
371. Find all x values in the interval [0, 2π]
where the function f
 
(x) = 2 cos x + sin
2 
x
has a horizontal tangent line.
372. Suppose that H is a function such that
′
=
H x
x
( ) 2 for x > 0. Find an expression for
the derivative of F x
H x
( )
( )
= [
]
3 .
357. f x
x
x
( )
cos
=
+
(
)
2
5
358. f x
x
x
x
( )
sin( )
cos( ) sin( )
=
+
π
π
π
359. f
 
(x) = cos(x sin x)
360. f x x
x
( )
sin
=
3
361. f x
x
x
( ) =
−
3 2
362. f
 
(x) = sec
2 
x + tan
2 
x
363. f x
x
x
( ) =
+
1
2
364. f x
x
x
( ) =
+
(
) +
2
3
4
1
5
365. f x
x
x
( ) =
−
(
) +
(
)
4
3
5
6
1
1