52 Part I: The Questions
350. Assuming that g is a differentiable function,
find an expression for the derivative of
f x
g x
x
( )
( )
=
3
.
351. Assuming that g is a differentiable function,
find an expression for the derivative of
f x
x
g x
( ) cos
( )
=
.
Using the Chain Rule
to Find Derivatives
352–370 Use the chain rule to find the derivative.
352. f x
x
x
( ) =
+
(
)
2
100
3
353. f
 
(x) = sin(4x)
354. f x
x
( )
sec
= +
1
3
355. f x
x x
( ) =
−
(
)
1
2
5
356. f x
x
( ) csc
=






1
2
342. f x
x
x
x
( ) sin
cos
=
+
4
2
343. Assuming that f and g are differentiable
functions, find the value of f
g






′
( )
5 if
f
 
(5) = –4, f
 
'(5) = 2, g(5) = –7, and g'(5) = –6.
344. f x
x
x
( ) = +
2
1
345. f x
x
x
x
( )
sin
cos
sin
=
+
346. f x
x
x
( ) = +
2
3
1
347. f x
x
x
( ) =
+
+
2
1
348. f x
x
x
( ) tan
sec
=
−
+
1
1
349. f x
x
x x
( ) =
+ 4