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
y(0) = 3 and y 0 (0) = 2
Question #
Find derivative of y = 3 cosh (5x) sinh (5x)
y = ln cosh (6x3 )
4y = 0
0) = 3 and y 0 (0) = 2
Question #
y = 3 cosh (5x) sinh (5x)
Find derivative of
y = ln cosh (6x3 )
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.
Question #
y 00 4y = 0
Of all the rectangles with a perimeter of 38 feet, find the dimensions of the one with the largest area.
y(0) = 3 and y 0 (0) = 2
y = 3 cosh (5x) sinh (5x)
y = ln cosh (6x3 )
y = 16
p
6 5
Question #
Find the coordinates of the point(s) on the curve
x2
p
A
y = p +y 00B 4y
x =0
x
y(0) = 3 and y 0 (0) = 2
5y = 25
y=
p
x2
y = 3 cosh (5x) sinh (5x)
x + 5 that are closest to the point (10, 0).
y = ln cosh (6x3 )
y = 16
p
x2
p
A
p
y=
+B x
x
6 5
5y = 25
Question #
A rectangle has one side on the x-axis and the upper two vertices on the graph of
should the vertices be placed so as to maximize the area of the rectangle?
11
y=
p
x2
x+5
y = 5e
3x2
. Where