Answers
Answer:
[tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}[/tex]
[tex]\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Calculus
Derivatives
Derivative Notation
eˣ Derivative: [tex]\displaystyle \frac{d}{dx}[e^x] = e^x[/tex]
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x \cdot e^x][/tex]
[tex]\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x \cdot e^{2x}][/tex]
Step 2: Differentiate
[tex]\displaystyle \frac{d}{dx}[e^{2x}][/tex]
[Derivative] Product Rule: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x]e^x + e^x\frac{d}{dx}[e^x][/tex][Derivative] eˣ Derivative: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = e^x \cdot e^x + e^x \cdot e^x[/tex][Derivative] Multiply [Exponential Rule - Multiplying]: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = e^{2x} + e^{2x}[/tex][Derivative] Combine like terms [Addition]: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}[/tex][tex]\displaystyle \frac{d}{dx}[e^{3x}][/tex]
[Derivative] Product Rule: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x]e^{2x} + e^x\frac{d}{dx}[e^{2x}][/tex][Derivative] eˣ Derivatives: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = e^x(e^{2x}) + e^x(2e^{2x})[/tex][Derivative] Multiply [Exponential Rule - Multiplying]: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = e^{3x} + 2e^{3x}[/tex][Derivative] Combine like terms [Addition]: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Related Questions
One month Amy rented 4 movies and 8 video games for a total of 61 dollars. The next month she rented 2 movies and 3 video games for a total of 24 dollars. Find the rental cost for each movie and each video game.
Rental cost for each movie: $?
Rental cost for each video game:$?
Answers
Answer:
Rental cost of movie is $6.50 ; Rental cost of video game is $2.25
Step-by-step explanation:
4m + 8v = 61 ........ (1)
2m + 3v = 24 ........ (2)
(1) - 2 × (2)
2v = 13
v = 6.5
2m + 3(6.5) = 24
2m = 24 - 19.5
m = 4.5 ÷ 2 = 2.25
Rental cost for each movie is $6.50
Rental cost for each video game is $2.25
Which equation(s) represents a nonproportional relationship? Select all that apply
O y = 3x
O y = 3x-2
O y=x+1
O y=-4x
O y=-2-4
Answers
Don’t click on the other comment, that link is a hack
Christopher is 20 years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years
ago, Ishaan was 3 times as old as Christopher.
How old is Christopher now?
Answers
what is the measure of angle k?
Answers
9514 1404 393
Answer:
59°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
∠N +∠L = 180°
(a +16) +(a -18) = 180
2a = 182 . . . . . . . . . . add 2
a = 91 . . . . . . . . . . . . divide by 2
Then the measure of angle M is ...
∠M = (a+30)° = (91 +30)° = 121°
and angle K is its supplement.
∠K = 180° -121°
∠K = 59°
PLEASE HELP
What is the length of the altitude of the equilateral triangle below?
Answers
What is the answer?1/3(x-10)=-4
Answers
Answer:
x=-11
Step-by-step explanation:
not entirely sure what it means by DBJ, but lets see..
i believe the answer is x=-11.
please resend the problem fixed
Jamie has 3 dogs, 4 cats, 2 lizards and 2 sisters. He wants to find the
percent of his pets that are lizards. Classify each statement as true or
false based on the information. *
True
False
The number of sisters is not
needed to find the percent of
pets that are lizards.
O
To find the percent of pets
that are lizards, 2 is the part
and 11 is the whole
ооо.
To find the percent of pets
that are lizards, 2 is the part
and 9 is the whole
Answers
2. False
3. True
Harper's house is 30 feet wide and 45 feet long. On a scale drawing, the house is 4 inches wide and 6 inches long, and Harper's bedroom is 1.2 inches wide and 1.6 inches long.
What are the actual measurements of Harper's bedroom?
Enter your answers in the boxes.
Answers
Answer:
9ft wide 12ft long
Step-by-step explanation:
Helpp I cant get the answer......Whats 6 divided by 2 ( 1 + 2)
Answers
Answer:
3
Step-by-step explanation:
Find the lateral surface area of the following prism: 5 cm 4 cm 5 cm 8 cm 6 cm LSA = [?] cm2 Enter
Answers
Answer:
Step-by-step explanation:
I was using 6×8 rectangle as a base of the triangular prism (as shows on the picture.
Let use the definition of a triangular prism and LSA = (5 + 5 + 6) × 8 = 128 cm²
The lateral surface area of the triangular prism is 128 square cm.
What is triangular prism?A triangular Prism is a pentahedron. It is a 3-D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The edges and vertices of the bases are joined with each other via three rectangular sides.
For the given situation,
The sides of the triangle are 5 cm, 6 cm, 5 cm.
The length of the prism = 8 cm
The formula for lateral surface area of triangular prism is
[tex]LSA=(perimeter)(length)[/tex]
On substituting the above values,
⇒ [tex]LSA=(5+6+5)(8)[/tex]
⇒ [tex]LSA=(16)(8)\\[/tex]
⇒ [tex]LSA=128[/tex]
Hence we can conclude that the lateral surface area of the triangular prism is 128 square cm.
Learn more about triangular prism here
https://brainly.com/question/15070306
#SPJ2
One of the games at the carnival was Spin the Pointer, which uses a spinner like the one pictured here. A carnival ticket that costs $1.00 is required to play the game. For each $1.00 ticket, a player spins the pointer once and receives the amount of money indicated in the sector where the pointer lands on the wheel. The spinner has an equal probability of landing in each of the 8 sectors.
a. Let X represent the profit for the player from one play of the game. Complete the table below for the probability distribution of X.
X -$1.00 $0.00 $4.00
P(X)
b. Find the expected value of the profit for the player from one play of the game. You may handwrite your calculations.
Answers
Answer:
(a)
[tex]\begin{array}{cccc}{X} & {-\$1.00} & {\$0.00} & {\$4.00} \ \\ {P(X)} & {0.75} & {0.125} & {0.125} & \ \end{array}[/tex]
(b)
[tex]E(x) = -\$0.25[/tex]
Step-by-step explanation:
Given
See attachment for spinner
Solving (a): Complete the table
The amount paid is: $1
From the attached image, we have:
$0 = 6; $1 = 1; $5 = 1
To get the profit, we subtract $1 from the possible outcomes of the spinner.
So, we have:
-$1.00 = 6; $0.00 = 1; $4.00 = 1
The probability of each is then calculated as:
[tex]P(-\$1.00) = \frac{6}{8} = 0.75[/tex]
[tex]P(-\$0.00) = \frac{1}{8} = 0.12[/tex]
[tex]P(-\$4.00) = \frac{1}{8} = 0.12[/tex]
So, the complete table is:
[tex]\begin{array}{cccc}{X} & {-\$1.00} & {\$0.00} & {\$4.00} \ \\ {P(X)} & {0.75} & {0.125} & {0.125} & \ \end{array}[/tex]
Solving (b): The expected profit E(x)
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
[tex]E(x) = -1.00 * 0.75 + 0.00 * 0.125 + 4 * 0.125[/tex]
[tex]E(x) = -\$0.25[/tex]
Rewrite in simplest form: 8(2x)
Answers
Answer:
Probably is 16x
Answer:
8×2x
Step-by-step explanation:
As u know that the bracket mean multiplication
A Hummingbird moves its wings at a rate of 5460 wingsbeats a minute. Write this rate in wingbeats per second?
PLEASE HELP
Answers
Answer:
60 seconds in a minute, so
5460 ÷ 60 = 91 beats per second
Which property justifies the statement below?
a(2b+c)=a(c+2b)
a. commutative property of addition
b. commutative property of multiplication
c. associative property of addition
d. distributive property
Answers
Answer:
d. distributive property
Step-by-step explanation:
please show all work i’ll mark brainliest
Answers
Answer:
a) P = 26 cm
b) A = 36 cm²
Step-by-step explanation:
perimeter is sum of all sides: 6+4+2+3+4+7 = 26
Area can be found by taking entire area, 7x6, then subtracting out the area of the missing piece, 2x3
A = 42 - 6 = 36 cm²
Answer:
Area is 36 and Perimeter is 26
Step-by-step explanation:
solving area:
4x6=24
3x4=12
24+12=36
solving perimeter:
6+4+2+3+4+7= 26
Which equation represents a line which is parallel to the y-axis?
X=-4y
Y=x-3
Y=-7
X=-8
Answers
Answer:
x = -8
Step-by-step explanation:
If the line is parallel to the y axis, that means it will be a vertical line.
Vertical lines have an equation of x = , because the line will only go through one x value.
They also will not have a slope, because their slope is undefined.
So, the correct answer is x = -8
24. A rectangle has a length of x +5 and a width of 2x-9. Using the formula for the perimeter of a rectangle wrote an expression to represent the perimeter of the rectangle in simplest form
Answers
Answer:
Perimeter = 6x-8
Step-by-step explanation:
a=x+5
b=2x-9
Perimeter = 2*(a+b)
Perimeter = 2*(x+5+(2x-9))
Perimeter = 2*(x+5+2x-9)
Perimeter = 2*(3x-4)
Perimeter = 6x-8
X+y= -4 2x -2y= 0 what best describes the solution to the system
Answers
Answer:
install photomath
Step-by-step explanation:
.............
What is the correct answer?
Answers
Unit 7 polygons hw 2 parallelograms
Please need this by tonight will give Brainly if it is all right
Answers
Can the real number -6 be classified as a rational number?
Answers
yes, -6 is a rational number
The measures of two complementary angles have a ratio of 2:3. What is the measure of the larger angle?
The measure of the larger angle is
°.
Answers
Step-by-step explanation:
complementary angles add up to 90
x +2/3x = 90
5/3x = 90
5x = 270
x = 54
the other angle is 36
double checking
54 * 2 ÷ 3 = 36
Will mark brainliest
Answers
x=140 is the answer #####
A car travels at an average speed of 68 mph how many miles does it travel in four hours and 30 minutes
Answers
Answer:
about 306 miles.
Step-by-step explanation:
68 times four and a half is 306.
hope this helped! :)
Answer:
306 miles.
Step-by-step explanation:
30 minutes = 0.5 miles.
Distance travelled = 68 * 4.5
= 306.
Ashley has 4 pairs of low-top sneakers, 7 pairs of high-top sneakers, 3 pairs of sandals, and 1 pair of boots. What is the ratio of the pairs of low-top sneakers to the total number of pairs of shoes
Answers
The ratio is 4:15
what is ratio?A ratio indicates how many times one number contains another.
Given:
low-top sneakers= 4
high-top sneakers= 7
sandals= 3
boots = 1
Total shoes= 15
Now,
low- top sneakers : totals shoes
=4:15
Learn more about ratio here:
https://brainly.com/question/23499990
#SPJ2
8. Lucy deposited $1,000 into an account that earns 5% compound interest, compounded annually. How much interest will Lucy earn after 10 years?
Answers
Answer:
5 dollars
Step-by-step explanation:
help with geometry question please
Answers
Answer:
Length of parallel side 2 = 2.91 km
Step-by-step explanation:
Given figure is a trapezoid
Given:
Area of trapezoid = 16.3 km²
Length of parallel side 1 = 5.9 km
Height of trapezoid = 3.7 km
Find:
Length of parallel side 2
Computation:
Area of trapezoid = [Sum of parallel side/2]Height
Area of trapezoid = [(a+b)/2]h
[(5.9 + b)/2]3.7 = 16.3
Length of parallel side 2 = 2.91 km
When point J (-14,6) is rotated 180 degrees around the origin, what is the resulting point J'? a (14,-6) b (-14,6) c (14,6) d (-14,-6)
Answers
Answer:
[tex]J' = (14,-6)[/tex]
Step-by-step explanation:
Given
[tex]J = (-14,6)[/tex]
[tex]R_0 = 180^\circ[/tex]
Required
Determine J'
When a point (x,y) is rotated 180 degrees around the origin, the new point is (-x, -y).
So:
[tex]J = (-14,6)[/tex]
[tex]J' = (14,-6)[/tex]
16. If (2x+3y)< (x+5y) or x < y, then which of the follwong is true?
Answers
Answer:
See explanation
Step-by-step explanation:
Given
[tex]2x + 3y < x + 5y[/tex]
[tex]x < y[/tex]
Required
Which option is true;
No option is given; so, I will just solve the inequality
[tex]2x + 3y < x + 5y[/tex]
Collect like terms:
[tex]2x - x < 5y - 3y[/tex]
Evaluate like terms
[tex]x < 2y[/tex]
This implies that:
[tex]x < 2y[/tex] and [tex]x < y[/tex]
18
Drag each label to the correct location on the tree diagram. Each label can be used more than once, but not all labels will be used.
Jolene can take elther of two roads to return home from school, road 1 or road 2. She can choose to walk, bike, or ride her scooter. She must
choose one road and one mode of travel. The sample space is given as a tree diagram. Complete the sample space.
road 1
scooter
walk
bike
walk
bike
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
returning home
road 2
2021 Edme
bike
Answers
Answer:
very left box- road 1
top right box- scooter
bottom right box- walk
Step-by-step explanation:
Answer: answer above me is correct
