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
9
C) 16h D)- 61
i
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
x + 2x) (4x 5 sin
8)
+
4
C)10 cos (2x)e (2x)x +2x
D)105x
cos2(2x)esin (2x)
h
i
15x4
2
5
3
2
8) 2 +2x + x 2
2A) (x + 2x) (4x
(36x ln (x) + x6 ) B)e3xx5(36x
ln (x) + x6 )
4
2
B) x15x
5 +2x +6x 2 6
x2
(36x ln (x ) + x )
2
D)e3x (x ln (x) + x6 )
h
i
15x5
2
5
3
2
C) (x Question
+ 2x) (4x
#: 8) x5 +2x + 3x 2
✓ ◆i
h
12
15x4
3
2
arccos
D) (x5Find
+ 2x)
(4x
8)
+
exact value x4 +2x
5x 2
2
✓ ✓
◆◆
11⇡
2
2
cos
A)ex (36x ln (x) + x6arcsin
) B)e3x
(36x 3ln (x) + x6 )
✓
✓ ◆◆
2
2
C)e3x (36x ln (x6 ) + x6 ) D)e3x (x ln1(x) + x6 )
sin 4 arccos
2
✓ ◆
1
1
y = tanarccos
(3x + 2)
2
Question #:
✓ ✓
◆◆
1
11⇡
tan (5x
cos + 6)
Find exact valuey =arcsin
3
✓
✓ ◆◆
1 5x
y = sine 4arcsin
(7x)1
arccos
5
2
y = tan
9
y = tan
1
(3x + 2)
1
(5x + 6)
1
y = e5x arcsin (7x)
5
8)2
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)
2
x5 +2x
x 2
4
15x
2
+
4
x +2x
5x 2
5
✓ 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◆
sin 4 arccos 1
arccos 2
2
✓ + 2)◆◆
y = tan✓ 1 (3x
11⇡
arcsin cos
3
1
y =✓
tan (5x +
✓ 6)◆◆
1
sin 4 arccos
2
1 5x
Question #:
Find derivative
y = e arcsin (7x)
5
1
y = tan
(3x + 2)
y = tan9 1 (5x + 6)
Question #:
1
y = e5x arcsin (7x)
5
Find derivative
9
10
Question #:
y = ln (arcsin (4x))
Find derivative
y = arctan (ln (3x
y = arcsin
y=
p
64
x2
⇣p
3
8))
2x2
+ 5 arcsin
✓
e10x
y = arcsin
10
◆
⌘
⇣x⌘
5