A)e arcsin (7x) +y =
x
C)e arcsin (7x) +
A) arcsin (4x)4p1
⇡
6
Quiz
18
B) 2⇡
34
16x2
C) ⇡3
C) arcsin (x)p1 16x2
⇡
Example
1: ⇡
B) 2⇡ C)
6
p
5x
p e
1 49x2
5x
3
3
5
64
⇣x⌘
B)e
(7x)
x2 5x+arcsin
5 arcsin
+
5
✓ 10x (7x)
◆ +
D)e arcsin
1 49x2
e
y = arcsin
1p
10
B)
p
7e5x
5x
5x
p7e
5 1 49x2
Math 1431
5x
p7e
2
5 LAB
1+49xsession
arcsin (4x) 1 16x2
D) ⇡4
D) arcsin (4x)4p1+16x2
D) ⇡4
3
2
Find
derivative of 1 y = sinh (4x + 10x )
5
25x2 +60x+36
B) 25x2 +60x+37
1
25x2 +60x+36
5
5 y = sinh ln (5x )
D) 25x2 +60x+37
e5x arcsin (7x) +
ex arcsin (7x) +
4p
arcsin (4x) 1 16x2
4p
arcsin (x) 1 16x2
5x
p e
1 49x2
y = (cosh (6x))x
B)e5x arcsin (7x) +
5x
p7e
5 1 49x2
y 5x
= A sinh (Cx) + B cosh (Cx)
p7e
5 1 49x2
D)e5x arcsin (7x) +
B) arcsin (4x)1p1 10
16x2
D) arcsin (4x)4p1+16x2
y = sinh (4x3 + 10x2 )
Example 2:
Find derivative of
y = sinh ln (5x5 )
y = (cosh (6x))x
y = A sinh (Cx) + B cosh (Cx)
10
5x
p7e
5 1+49x2
11
y = sinh (4x + 10x )
Example 3:
y = sinh ln (5x5 )
Find derivative of
y = (cosh (6x))x
y = A sinh (Cx) + B cosh (Cx)
10
y = (cosh (6x))x
Example 4:
Determine A, B, and C so that
y 00
y = A sinh (Cx) + B cosh (Cx)
4y = 0
10
y(0) = 3 and y 0 (0) = 2
11
satisfies the conditions
p
6 5
0
y(0) = 3 and y (0) = 2
Question #
5y = 25
x2
p
y = x+5
Find derivative of y = 3 cosh (5x) sinh (5x)
2
y = 5e 3x
= ln cosh
(6x3 )2 (5x) + cosh2 (5x))
A)15(sinh2 (5x) + cosh2 y(5x))
B)3(sinh
5y = 25
C)15(sinh2 (5x)
cosh2 (5x))
D)(sinh2 (5x) + cosh2 (5x))
y=
4y = 0
p
x+5
y = 5e
0) = 3 and y 0 (0) = 2
A)15(sinh2 (5x) + cosh2 (5x))
Question #
x2
3x2
B)3(sinh2 (5x) + cosh2 (5x))
y = 3 cosh (5x)
11 sinh (5x)
2
2
C)15(sinh
(5x)
cosh
(5x))
Find derivative of y = ln cosh (6x )
3
A)
18x2 cosh (6x3 )
sinh (6x3 )
B)
18x2 sinh2 (6x3 )
cosh (6x3 )
C)
18x2 sinh (6x3 )
cosh (6x3 )
D)
18x2 sinh (6x3 )
cosh2 (6x3 )
D)(sinh2 (5x) + cosh2 (5x))
11
11
Quiz 19
= 3 cosh (5x) sinh (5x)
Example 5:
y =Find
ln cosh
(6x3 )
the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve
y = 16
11
x2
Example 6:
Of all the rectangles with an area of 420 square feet, find the dimensions of the one with the smallest perimeter.
Example 7:
Of all the rectangles with a perimeter of 52 feet, find the dimensions of the one with the largest area.
Example 8:
A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of
the playground. 640 feet of fencing is used. Find the dimensions of the playground that will enclose the
greatest total area.
y = 16
x2
Example 9:
Find A and B given that the function
p
p
A
p
y=
+B x
x
6 5
11
p
has a minimum value of 6 5 at x = 5.
y=p
p
6 5
Example 10:
Find the coordinates of the point(s) on the curve
5y = 25
11
x2
that are closest to the origin.
2
3)
2
3
sinh (6x
C) 18xcosh
3
Question(6x
# )
sinh (6x )
D) 18x
2
3)
y 00 4y = 0
cosh
Of all the (6x
rectangles
with a perimeter of 40 feet, find the dimensions of the one with the largest area.
A)169
B)144
y(0) = 3 and y 0 (0) = 2
C)121 D)100
y = 3 cosh (5x) sinh (5x)
11
y = ln cosh (6x3 )
x2
y = 16
p
6 5
Question #
Find the coordinates of the point(s) on the curve
A)169 B)144 C)121 D)100
⇣ p ⌘
⇣ p ⌘
⇣ p ⌘
45
13
13
19
A) 2 ; 2
B) 2 ; 2
C) 19
; 258
2
p
A
y = p +y 00B 4y
x =0
x
y(0) = 3 and y 0 (0) = 2
x2
5y = 25
y=
D)
⇣
p
17
;
2
y = 3 cosh (5x) sinh (5x)
x + 5 that are closest to the point (10, 0).
p
35
2
⌘
y = ln cosh (6x3 )
p
y = 16
x2
p
A
p
y=
+B x
x
6 5
5y = 25
Question #
A)169 B)144 C)121 D)100
⇣ p has
⌘ one side
⇣ on
⌘ x-axis ⇣and the
⌘
A rectangle
two⇣ vertices
on the graph of
p the
p upper
p ⌘
45
13
58
35
13
19
19
17
should
be placed
to maximize
A) 2 the
; 2verticesB)
; 2 so as C)
; 2 the area
D) of 2the
; rectangle?
2
2
2
11
⇣
⌘
⇣
⌘
⇣
⌘
⇣
⌘
1
5
1
5
1
3
1
3
p ;p
p ;p
A) p6 ; pe and
B) p7 ; pe and
e
e
6
7
⇣
⌘
⇣
⌘
⇣
⌘
⇣
⌘
p1 ; p3
p1 ; p5
C) p14 ; p3e and
D) p18 ; p5e and
e
e
4
8
y=
p
x2
x+5
y = 5e
3x2
. Where