50 Part I: The Questions
319. f
 
(x) = (sec x)(x + tan x)
320. f x
x
x
x
( )
csc
=
+
(
)
2
321. f
 
(x) = 4x
3
sec x
322. f x
x
x
( ) cot
= 1 2
323. Assuming that g is a differentiable function,
find an expression for the derivative of
f
 
(x) = x
2
g(x).
324. Assuming that g is a differentiable function,
find an expression for the derivative of
f x
x g x
x
( )
( )
=
+
1
2
.
325. Find (fg)'(3) if f
 
(3) = –2, f
 
'(3) = 4, g(3) = –8,
and g
 
'(3) = 7.
326. f
 
(x) = x
2
cos x sin x
Using the Product Rule
to Find Derivatives
312–331 Use the product rule to find the derivative
of the given function.
312. f
 
(x) = (2x
3
+ 1)(x
5
– x)
313. f
 
(x) = x
2 
sin x
314. f
 
(x) = sec x tan x
315. f x
x
x
( ) cos
=
316. f
 
(x) = 4x csc x
317. Find (fg)'(4) if f
 
(4) = 3, f
 
'(4) = 2, g(4) = –6,
and g
 
'(4) = 8.
318. f x
x
x
( )
g( )
=
3