5
3
D) (x + 2x) (4x
8)
2
h
2
15x4
x4 +2x
2
5x 2
+
i
2
A)ex (36x ln (x) + x6 )
B)e3x (36x ln (x) + x )
2
2(x) = (x 6 17)6
C)f
3xQuiz
17
4
D)f (x)
3x2 = (x
A)-6
B)-6 1: C) 16
Example
D)- 61
C)e
Math 1431
6 LAB session 10
(36x ln (x ) + x )
D)e
3
5x)
6
(x ln (x) + x )
p !
3
5 sin (2x)
5 sin (2x)
arcsin
Find
the
exact
value
A)5 cos (2x)e
B)10 cos (x)e
2
✓ ✓ ◆◆
8⇡ sin (2x)
C)10 cos (2x)e5 sin (2x) D)10 cos (2x)e
arccos sin
3i
h 4
15x
2
✓ ◆◆
A) (x5 + 2x)3 (4x 8)2 x✓
5 +2x + x 2
1
sin 4 arccos
2
15x4
2
B)
x5 +2x
+
x 2
i
f (x)2 h=15x
(x55 + 2x)23 (4x
8)2
(x45 ++2x)23 (4x
D) (x + 2x) (4x f (x)
8)2 =x15x
4 +2x
5x 2
8)2
f (x) = (x5 + 2x)3 (4x
8)2
C) (x5 + 2x)3 (4x
5
3
8)
+
3x 2
h
2
i
2
A)ex (36x ln (x) + x6 )
2
x5 +2x
B)e3x (36x ln (x) + x6 )
C)e3x (36x ln (x6 ) + x6 )
2
D)e3x (x ln (x) + x6 )
9
p !
3
arcsin
2
Example 2:
✓ ✓ ◆◆
8⇡
Find the exact value arccos sin
3
✓
✓ ◆◆
1
sin 4 arccos
2
f (x) = (x5 + 2x)3 (4x
8)2
f (x) = (x5 + 2x)3 (4x
8)2
f (x) = (x5 + 2x)3 (4x
8)2
9
8⇡
3
✓
✓ ◆◆
1
sin 4 arccos
2
arccos sin
Example 3:
Find the exact value
(x) = (x
17)2
4
3
D)f (x)
(x(x
5 5x)
f (x)= =
+ 2x)3 (4x
B)-6
C) 16
D)- 61
cos (2x)e5 sin (2x)
f (x) = (x5 + 2x)3 (4x
8)2
B)10 cos (x)e5 sin (2x)
5
3
f (x)
(x sin+(2x)
2x) (4x
D)10
cos=
(2x)e
h
i
15x4
2
2
8) x5 +2x + x 2
17)2 D)f (x) = (x4 5x)3
0 cos (2x)e5 sin (2x)
x5 + 2x)3 (4x
C)f (x) = (x
15x4
2
5 +2x + x 2
A)-6 B)-6
8)2
8)2
9
C) 16h D)- 61
i y = ln (arcsin (4x))
15x5
2
x5 + 2x)3 (4x 5 sin8)(2x)
+ 3x2 2 5 sin (2x)
x5 +2x
A)5 cos (2x)e
B)10 cos (x)e
h
i
15x4
2
5
3
2
y = arctan (ln (3x 8))
x + 2x) (4x 5 sin
8)
+
4
C)10 cos (2x)e (2x)x +2x
D)105x
cos2(2x)esin (2x)
h
i
⇣p
⌘
15x4
2
5
3
2
8) 2 +2x + x y2 = arcsin
2A) (x + 2x) (4x
3 2x2
(36x ln (x) + x6 ) B)e3xx5(36x
ln (x) + x6 )
4
2
B) x15x
5 +2x +6x 2 6
x2
(36x ln (x ) + x )
⇣ ⌘
x
D)e3x (x ln (x)p+ x6 )
2 + 5 arcsin
h
i
y
=
64
x
15x5
2
5
C) (x5Question
+ 2x)3 (4x
8)
+ 3x2 2
#:
x5 +2x
✓ ◆yi = ln (arcsin
✓ (4x))
◆
h
10x
1
4
15x
3
e
D) (x5Find
+ 2x)
(4xvalue
8)2 arccos
+ 5x2 2
exact
x4 +2x
y
=
arcsin
2
10
✓ ✓
◆◆
y11⇡
=
(ln (3x 8))
⇡
2⇡
⇡3x2
⇡ arctan
6arcsin
6
x2 A)
B)
C)
D)
cos
A)e (36x6ln (x) + 3x ) B)e3 (36x 3ln
4 (x) + x )
⇣p
⌘
✓
✓
◆◆
2
2
2
⇡ ln (x6 ) 2⇡
⇡ 3x (xyln1
⇡
C)e3x A)
(36x
+ x6 ) C)
D)e
(x)
+ x6 )
=
arcsin
3
2x
B)
D)
6
3 sin 4 arccos
3
4
2
⇣x⌘
✓ ◆
p
2
y1 (3x
= +164
y = tanarccos
2) x + 5 arcsin
5
2
Question #:
✓ ✓
◆◆
✓ 10x ◆
1
11⇡
e
tan (5x
cos +y 6)
Find exact valuey =arcsin
=
arcsin
3
10
✓
✓
◆◆
1
1
⇡
2⇡ y = e⇡5x arcsin⇡(7x)
A) 6 B) 3
C)
D)
sin
4
arccos
4
5 3
2
A) ⇡6
B) 2⇡
3
2
⇡
C)
D)1 ⇡4 + 2)
y=
3 tan (3x
9
y = tan
1
(5x + 6)
1
y = e5x arcsin (7x)
5
arcsin
cos i
h
3
4
2
8)2 x15x
+
5 +2x
x 2 ✓ ◆◆
✓
Example
4:
1
sin 4 arccos
Find derivative for
2 all functions below
h
i
15x5
2
2
8) yx=
5 +2x
tan+ 13x(3x
2 + 2)
h
i
15x4
2
2
8) x4 +2x + 5x 2
y = tan 1 (5x + 6)
6
)
x
2
B)e13x 5x
(36x ln (x) + x6 )
y = e arcsin (7x)
5 2
6
+ x ) D)e3x (x ln (x) + x6 )
p !
3
2
✓ ✓ ◆◆
8⇡
arccos sin
3
✓
✓ ◆◆
1
sin 4 arccos
2
9
arcsin
y = tan (3x + 2)
1
y = 7e2x arcsin (3x)
y = ln (arctan (6x + 15))
9
y = 7e arcsin (3x)
y = ln (arctan (6x + 15))
9
y = arctan (ln (3x
y = arcsin
y=
p
64
⇣p
3
8))
2x2
x2 + 5 arcsin
✓
e10x
y = arcsin
10
◆
⌘
⇣x⌘
5
y = arctan (ln (3x
y = arcsin
y=
p
⇣p
8))
2x2
3
x2 + 5 arcsin
64
y = arcsin
✓
e10x
10
◆
y = arctan (ln (3x
y = arcsin
y=
p
64
⇣p
3
⌘
⇣x⌘
5
8))
2x2
x2 + 5 arcsin
y = arcsin
10
✓
e10x
10
◆
⌘
⇣x⌘
5
5
3
(x + 2x) (4x
8)
x5 +2x
x 2
4
15x
2
+
4
x +2x
5x 2
5
2
✓ 10x ◆
+ x2 2
e
y = arcsin
i
6 10h 3x52
6
x2
e(x5(36x
ln
(x)
+
)
B)e
(36x
ln
(x)
+
)
15x
2
3
2
x
x
+ 2x) (4x 8) x5 +2x + 3x 2
2
h
i
3x2
4
e3x5(36x ln3(x6 ) + x6 ) 2 D)e
(x ln2 (x) + x6 )
15x
(x + 2x) (4x 8) x4 +2x + 5x 2
15x4
x5 +2x
✓ ◆
1
2
2
arccos
6
ex (36x ln (x) + x6 ) B)e3x (36x ln
2 (x) + x )
✓ ✓
◆◆
11⇡
6
3x2
6
3x2
e (36x ln (x ) + x ) arcsin
D)e cos
(x ln (x) + x6 )
3
✓
✓ ◆◆
✓ 1◆
= ln (arcsin
1 (4x))
sin 4y arccos
arccos 2
y = ln (arcsin (4x))
y = arctan (ln (3x
y = arcsin
y=
p
64
⇣p
B) 2⇡
3
C) ⇡3
D) ⇡4
2
y = arctan
(ln
(3x
8)) (4x))
y=
(arcsin
A) ⇡6 B) 2⇡
C) ⇡3 D) ⇡4
✓ln
◆◆
3
y = tan✓ 1 (3x
+
2)
11⇡ ⌘
arcsin cos⇣p
5
1
y = arcsin
3 3 2x2
A) 25x2 +60x+36
B) 25x2 +60x+37
y = arctan (ln (3x 8))
y =✓
tan 1 (5x +
✓ 6)◆◆⇣ x ⌘
p
1
5
1⇣
C) ⌘
D) 25x2 +60x+37
y = 64 x2 + 5 arcsin
2 +60x+36
25x
p5
sin 4 arccos
2x2
1 5xy = arcsin
✓ 2 ◆ 3
Question #:
Find derivative
10x
y = e arcsin (7x)
5y = arcsin e
⇣x⌘
y = tanp1 (3x 10
+2 2)
= 64 x + 5 arcsin
A) ⇡6 B) 2⇡
C) ⇡3 D) ⇡y
3
4
5
A) ⇡6 B) 2⇡
C) ⇡3 yD)
=⇡4 tan9 1 (5x + 6)✓ e10x ◆
3
y = arcsin
Question
5 #:
1
10
A) 2
B) 2
25x +60x+36
⇡
Find
A)
C) 6
25x +60x+37
1 5x⇡
e 4 arcsin (7x)
D)
5
25x +60x+37
2⇡
y ⇡3=5
derivative
C)
1 B) 3
D) 2
2
25x +60x+36
2⇡
⇡ 5x
p e⇡
A)e⇡5x arcsin
+C)
arcsin (7x) + 5p17e 49x
A)
B) (7x)
D)B)e
1 349x
6
3
4
5x
5x
2
C)ex arcsin
5 (7x) +
A) 25x2 +60x+36
1
C) 25x2 +60x+36
5x
p7e
5 1 49x2
5x
1D)e
9 arcsin (7x) +
B) 25x2 +60x+37
2
5x
p7e
5 1+49x2
5
D) 25x2 +60x+37
10
5x
p e
1 49x2
5x
B)e5x arcsin (7x) +
p7e
5 1 49x2
x
p7e
C)e
arcsin
(7x)
+
D)e5x arcsin (7x) +
y
=
Find derivative
5ln1(arcsin
49x2 (4x))
p7e
5 1+49x2
5x
A)e arcsin (7x) +
Question #:
5x
A) arcsin (4x)4p1
y = arctan (ln (3x
C) arcsin (x)4p1
16x2
16x2
B) arcsin (4x)1p1
⇣p 4p ⌘ 2
D) arcsin
(4x) 1+16x
y = arcsin
y=
p
8))16x2
2x2
3
10
64
x2
+ 5 arcsin
✓
10x
◆
⇣x⌘
5
5x
2x2
x2 + 5 arcsin
y = arcsin
A) ⇡6
3
8))
10
✓
e10x
10
◆
⌘
⇣x⌘
5