Math 113 – Homework 6 – Solutions

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Math 113 – Homework 6 – Solutions
Due: 15 December 2005 Thursday.
Find the derivatives of the given functions with respect to x and write your answers in the
spaces provided. Do not simplify. Leave your answer in a format which is easy to read.
1
f (x) = xx
2
f (x) = (ln x)ln x
3
f (x) = xcos x
Z
4
tan x
f (x) =
√
f 0 (x) = xx (ln x + 1)
1
1 1
f 0 (x) = (ln x)ln x ( ln ln x + ln x
)
x
ln x x
f 0 (x) = xcos x (− sin x ln x + cos x
1 + t3 dt f 0 (x) =
p
1 + tan3 x sec2 x −
√
1
)
x
1 + sec3 x sec x tan x
sec x
5
f (x) = sec x + ln tan x
1
x
f 0 (x) = sec x tan x +
f 0 (x) = sin
1
sec2 x
tan x
1
1 −1
+ x cos
x
x x2
6
f (x) = x sin
7
x2 + 1
f (x) = 3
x +1
8
f (x) = (cos x)(ln x)
f 0 (x) = − sin x ln x + cos x
9
f (x) = (cos x)2 ln x
f 0 (x) = 2(cos x)(− sin x) ln x + (cos x)2
10
f (x) = (cos x)2 (ln x)3
2x(x3 + 1) − (x2 + 1)(3x2 )
f (x) =
(x3 + 1)2
0
1
x
1
x
f 0 (x) = 2(cos x)(− sin x)(ln x)3 + (cos x)2 3(ln x)2
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