51
Chapter 5: The Product, Quotient, and Chain Rules
334. f x
x
x
( ) sin
cos
=
−
+
1
1
335. f x
x
x
x
( ) =
+
+
5
3
1
336. Assuming that f and g are differentiable
functions, find the value of f
g






′
( )
4 if
f
 
(4) = 5, f
 
'(4) = –7, g (4) = 8, and g '(4) = 4.
337. f x
x
x
( ) = +
+
2
3
5
338. f x
x
x
x
( ) =
− +
2
2
3
2 1
339. f x
x
x
( ) sin
=
3
340. f x
x
x
x
x
( )
(
)(
)
(
)(
)
=
−
+
−
+
1
2
3
1
341. f x
x
x
( )
sec
sec
= +
1
327. Assuming that g is a differentiable function,
find an expression for the derivative of
f x
xg x
x
( )
( )
=
+
2
.
328. f x
x
x
x
( )
(tan )
=
−






1 2
2
329. f x x x x
x
x
( )
cos
= − 2
3
2
330. Assuming that g is a differentiable function,
find an expression for the derivative of
f x
g x
x
( )
( )
=
4
5
.
331. Assuming that g and h are differentiable
functions, find an expression for the
derivative of f x
x h x
x
( ) g( ) ( ) sin
= [
]
.
Using the Quotient Rule
to Find Derivatives
332–351 Use the quotient rule to find the derivative.
332. f x
x
x
( ) =
+
+
2 1
3
4
333. f x
x
x
( ) = +
2
5
2