Answers to Practice Problems on Differentiation Most of the answers

Answers to Practice Problems on Differentiation
Most of the answers are given in a MINIMALLY simplified form (such as
combining the constants). If you solve the problem correctly, you should be
able to see that your answer matches the answer posted.
1) 2x + 14(2x + 3)6
2) 25 (2x − 1)−4/5
3) cos(2x) − 2x sin(2x)
4) 2x cos(2x) − 2x2 sin(2x)
√
− 3 x · sin(3x)
5)
cos(3x)
√
2 x
6)
4√
3
x cos(4x)
3
√
3
− 4 x4 · sin(4x)
7) 2x · sin(4x) + 4x2 · cos(4x)
8) 8(2x − 3)3 · tan(4x) + 4(2x − 3)4 · sec2 (4x)
9) 4x3 sec(x2 + 1) + 2x5 sec(x2 + 1) tan(x2 + 1)
10)
2x cos(2x)−sin(2x)
x2
11) cos
12)
1
2
2x+cos x
x2 −7
sin
2x+1
x3 −6x
·
(2−sin x)(x2 −7)−2x(2x+cos x)
(x2 −7)2
−1/2
· cos
2x+1
x3 −6x
·
2(x3 −6x)−(2x+1)(3x2 −6)
(x3 −6x)2
13) 15 sin2 (5x) · cos(5x)
14) 15 sec3 (5x) · tan(5x)
15) 15 sec3 (tan(5x)) · tan(tan(5x)) · sec2 (5x)
16) 4 tan3
17) 2 cos
x
sin x
x
sin x
· sec2
x
sin x
·
− (2x + 1) sin
18) (2+3 sec2 x) cos2
x
sin x
sin x−x cos x
sin2 x
x
sin x
·
sin x−x cos x
sin2 x
−2(2x+3 tan x) cos
x
sin x
·sin
x
sin x
·
sin x−x cos x
sin2 x
19) −24 cos2 (tan2 (4x)) · sin(tan2 (4x)) · tan(4x) · sec2 (4x)
20)
√
15 tan2 (5x−2)·sec2 (5x−2) x3 −sin x− 12 tan3 (5x−2)·(x3 −sin x)−1/2 ·(3x2 −cos x)
x3 −sin x
21)
3 sec3 (sin(x2 +1)+2x)·tan(sin(x2 +1)+2x)·(2x cos(x2 +1)+2)·
x3 +cos2 (3x)
√
x3 +cos2 (3x)−
− 12 (x3 +cos2 (3x))−1/2 ·(3x2 −6 cos(3x)·sin(3x)) sec3 (sin(x2 +1)+2x)
x3 +cos2 (3x)
22) 3 sin2
 √
·
√
x
x2 +cos x−6 cos(2x−1)
3x2 −sec(2x)
· cos
√
x
x2 +cos x−6 cos(2x−1)
3x2 −sec(2x)
·
x2 +cos x−6 cos(2x−1)+ x2 (x2 +cos x−6 cos(2x−1))−1/2 ·(2x−sin x+12 sin(2x−1)) (3x2 −sec(2x))−
(3x2 −sec(2x))2
√
−(6x−2 sec(2x) tan(2x))·x x2 +cos x−6 cos(2x−1)
(3x2 −sec(2x))2
23) − cos(cos(tan(sec x))) · (sin(tan(sec x))) · (sec2 (sec x)) · sec x · tan x
24)
− cos(cos x)·sin x·tan x·sec x−sin(cos x)·(sec3 x+tan2 x sec x)
tan2 x·sec2 x