Mathematics High School

What is the derivative of e^(2x)

I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.

Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/

Answers

Answer 1
Using the chain rule: The derivative of e^u is (e^u)(u').  Notice that e^u is rewritten exactly as is and then multiplied by the derivative of the exponent.  
Let u=2x. So u'=2  
So the derivative of e^u is e^(2x)*2 This can also be written as 2e^(2x).

Related Questions

The graph below shows the height of a kicked soccer ball f(x), in feet, depending on the distance from the kicker x, in feet: Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height? (6 points) Part B: What is an approximate average rate of change of the graph from x = 22 to x = 26, and what does this rate represent? (4 points

Answers

the complete question in the attached figure

part A

the x intercept 0 is the point where the ball was hit, the x intercept 20 is the point where the ball fell back to the ground, 20 feet away from the kicker.

the function is increasing in the interval x∈(0, 10) and decreasing in x∈(10, 20) 
this means that the height is increasing in the interval  (0, 10) and decreasing as x goes through the interval (10,20)
the distance from the kicker is increasing during the whole interval (0, 20)

part B

the rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases or increases in the interval 

x =[A, B]

from x = 22 to x = 26-------------- > the function does not exist


Carolyn has cut a piece of ribbon 29 centimeters long from a roll. which instrument would she use to measure the length of the piece of ribbon?

Answers

Final answer:

Carolyn would use a ruler to measure the length of the piece of ribbon.

Explanation:

To measure the length of a piece of ribbon, Carolyn would use a ruler as the instrument. A ruler is a tool used for measuring small items and distances. It is commonly used for measuring in inches, which is the appropriate unit for short lengths like a piece of ribbon. Carolyn can align one end of the ribbon with the zero mark on the ruler and then extend the ribbon along the ruler to measure its length accurately.

The ruler's precision in measuring small distances, typically in inches, allows Carolyn to obtain a detailed and accurate measurement for the ribbon's length. Aligning the ribbon's end with the ruler's zero mark ensures a standardized starting point for consistency in measurements. This straightforward method showcases the practicality and ease with which rulers facilitate precise length measurements, making them essential tools for tasks requiring accuracy in determining dimensions.

Part 1.] Identify the following series as arithmetic, geometric, both, or neither. Includes picture

Part 2.] Evaluate C(3, 3)
A.] 1
B.] 6
C.] 24

Part 3.] Evaluate C(6,3)
A.] 20
B.] 120
C.] 720

Part 4.] How many subsets of four elements each exist in a set of seven elements?
A.] 4!
B.] C(7, 4)
C.] P(7, 4) 

Part 5.] What is the probability of having 3 children that are all boys?
A.] [tex] \frac{1}{2} [/tex]
B.] [tex] \frac{1}{8} [/tex]
C.] [tex] \frac{3}{8} [/tex]

Answers

These are five questions and five answers.

Part 1.] Identify the following series as arithmetic, geometric, both, or neither. Includes picture

Answer: arithmetic

Justification:

The arithmetic series are those in which the distance (difference) between any consecutive terms is constant, so you can find the term An adding the difference to the previous term, A(n-1).

In this case the series is:

∞
∑ (3 + na) =>
n=1

Term1: 3 + a
Term2: 3 + 2a
Term3: 3 + 3a
Term3: 3 + 4a

As you see, the difference between two consecutive terms is a, which shows that it is an arithmetic series.


Part 2.] Evaluate C(3, 3)
A.] 1
B.] 6
C.] 24

Answer: option A) 1.

Explanation:

The formula for combinations is Cm,n = m! / [n! (m - n)! ]

So, for C3,3, C3,3 = 3! / [3! 0!] = 3! / 3! = 1.

From this you might learn that Cm,m for any m is always 1.

Part 3.] Evaluate C(6,3)
A.] 20
B.] 120
C.] 720

Answer: option A) 20

Explanation:

Use the same formula, Cm,n = m! / [n! (m - n)! ]

C6,3 = 6! / [3! 3! ] = 6*5*4 / (3*2*1) = 5*4 = 20

Part 4.] How many subsets of four elements each exist in a set of seven elements?
A.] 4!
B.] C(7, 4)
C.] P(7, 4) 

Answer: option B) C(7,4)

Explanation

You have to select collections of 4 elements from a set of 7 elements, and must realize that the order is irrelevant, i.e. it is the same the set ABCD as the set ACBD or DCAB or any combination of those four elements. So, the answer is a combination and not a permutation.

The number of subsets of 4 elements that you can form with 7 elements is: C(7,4), which is the option B.

Part 5.] What is the probability of having 3 children that are all boys?
A.] 1/2
B.] 1/8
C.] 3/8

Answer: option B: 1/8

Explanation:

The number of possible outcomes is 2 * 2 *  2 = 8

Only one of those outcomes is for all boys = 1

Therefore the probability is 1/8

You can see that representing the possible outcomes using B for boys and G for girls:

1) BBB (three boys)
2) BBG

3) BGB
4) BGG

5) GBB
6) GBG

7) GGB
8) GGG

Those are the 8 possible outcomes and as seen only one is for 3 boys.

Nicholas used a $10 bill to pay for a granola bar that only costs p dollars. How much change did Nicholas receive from the cashier?

Answers

10 - p.
Nicholas would have spent $p, so he has $p less than $10!
you can subtract 10 dollars by the p then you will get your answer 10-p=10p since you can't subtract a number by a letter.

if you pay $26.50 for an item, including 6% sales tax, what was the original price?

Answers

The original price was $24.91
You can do this by dividing by 1.06

26.5/1.06 = 25.00 dollars. You can check this by figuring out the sales tax separately

25 * (6/100) = 1.50

If you add 1.50 to 25 dollars, you get 26.5 just as you should.

WILL GIVE A BRAINLEST

What is the solution of x+4/2x-1<0 ?

Answers

To solve the inequality x + 4/2x - 1 < 0, first find the critical value x = 1/2. Then, test the intervals to determine the solution set x < 1/2.

To find the solution of the inequality x + 4/2x - 1 < 0, we can follow these steps:

First, find the critical values by setting the denominator, 2x - 1, equal to zero and solve for x. The critical value is x = 1/2.

Next, test the intervals created by the critical value in the original inequality x + 4/2x - 1 < 0. This helps determine the solution set which is x < 1/2.

Quadrilateral ABCD ​ is inscribed in this circle.

What is the measure of angle A?



Enter your answer in the box.


°

Answers

The answer to this is 65. 

Remember that the angles opposite of each other equal to 180. So a+c=180 and b+d=180. 

First, we solve for x. Since we know that b and d equal to 180, we subtract 148 from 180. 
180-148=32. x=32. 

Then we plug that in the expression for angle a. 
2x+1 becomes 2(32)+1
2*32=64
64+1=65.
a=65

A pillow that usually costs $20 is marked down 45%. Table Use the table to find the new price of the pillow. $9 $11 $29 $33

Answers

It would now cost $11. 45% of 20 is 9, therefore, you would subtract 9 from 20 (since it is getting marked down). 

Answer:

$11

Step-by-step explanation:

20-9=11

In the diagram a || b. Use the diagram to answer the question. (Diagram not to scale.) Name the interior angle to 7
A. 1
B. 2
C. 6
D. 4

Answers

thats wrong it is 2 b

If two figures are congruent, their perimeters are equal true or false?

Answers

This is true. The term congruent means that the shape is of exactly equal size. If this is true, then every side length would match for each shape. If this is true, the perimeter would also be exactly the same for each shape. Think of something that is congruent as being an exact copy of the original, with no change in size or shape.

A photographer enlarges a photo by using a scale of 5. The length of the original photo is 7 in. What is the length of the enlarged photo? Enter your answer in the box.

Answers

The answer is 35, i hope i helped if you have any questions just comment ill respond as soon as possible

Answer:

35

Step-by-step explanation:

35

Are the two triangles congruent?

Answers

Quick answer: No <<====
First: The 7 must be opposite the same size angle in both triangles for conguency.
Second: It does not look like these triangles have any angles in common.

What is the maximum number of distinct lines that can be drawn through 10 distinct points if no 3 of the points are collinear?

Answers

10 objects chosen 2 at a time can be chosen
.. 10*9/(2*1) = 45 ways

45 distinct lines can be drawn

Need help ASAP WILL GIVE TEN POINTS FIVE QUESTIONS-
1

What is the solution to the inequality?

6x−5>−29

A ​ x>−4 ​
B​ x<4 ​
C ​ x>4 ​
D​ x<−4 ​
2

What is the solution to the inequality?

−4x−8>−20
A​ x>3 ​
B​ x>−3 ​
C​ x<−3 ​
D​ x<3 ​

3Solve.

−4.2y+2.1>−2.52


Drag and drop a number or symbol into each box to show the solution.
< > 0.1 1.1 4.62 −4.62


Y.(number) (number)



4 Solve.

−12x+13>35

Drag and drop a number or symbol into each box to show the solution.
< > −8/15 −4/15 4/15 8/15

x (number) (number)

What is the solution set?

−2.8x+5.6<8.4

Enter your answer in the box.

x (answer) plz help and ty

Answers

The answer for 
1) x>-4
2)x<3
3)y<1.1
4)x<-11/6
5)x>-1
HOPE THIS HELP

Answer:

Part 1) Option A [tex]x>-4[/tex]

Part 2) Option D [tex]x<3[/tex]

Part 3) [tex]y < 1.1[/tex]  

Part 4) [tex]x<-8/15[/tex]

Part 5) [tex]x>-1[/tex]

Step-by-step explanation:

Part 1) we have

[tex]6x-5>-29[/tex]

[tex]6x>-29+5[/tex]

[tex]x>-24/6[/tex]

[tex]x>-4[/tex]

Part 2) we have

[tex]-4x-8>-20[/tex]

[tex]-4x>-20+8[/tex]

[tex]-4x>-12[/tex] -----> Multiply by [tex]-1[/tex]  both sides

[tex]4x<12[/tex]

[tex]x<12/4[/tex]

[tex]x<3[/tex]

Part 3) we have

[tex]-4.2y+2.1 >-2.52[/tex]

[tex]-4.2y >-2.52-2.1[/tex]

[tex]-4.2y >-4.62[/tex] ----> Multiply by [tex]-1[/tex]  both sides

[tex]4.2y < 4.62[/tex]

[tex]y < 1.1[/tex]

Part 4) we have

[tex]-(1/2)x+(1/3)>3/5[/tex]

[tex]-1/2x>(3/5)-(1/3)[/tex]

[tex]-1/2x>4/15[/tex] ---> Multiply by [tex]-1[/tex]  both sides

[tex]1/2x<-4/15[/tex]

[tex]x<-8/15[/tex]

Part 5) we have

[tex]-2.8x+5.6< 8.4[/tex]

[tex]-2.8x< 8.4-5.6[/tex]

[tex]-2.8x< 2.8[/tex] ---> Multiply by [tex]-1[/tex]  both sides

[tex]2.8x>-2.8[/tex]

[tex]x>-2.8/2.8[/tex]

[tex]x>-1[/tex]

A toy rocket is launched from a platform 42 feet above the ground at a speed of 91 feet per second. The height of the rocket in feet is given by the polynomial −16t^2 + 91t + 42, where t is the time in seconds. How high will the rocket be after 3 seconds? HELP ASAP!!

A. 122 feetB. 218 feetC. 93 feetD. 2570 feet

Answers

Lets get started!

height = -16t² + 91t + 42 
After 3 sec means, t = 3, so we substitute t with 3

H = -16(3)² + 91(3) + 42
    = -144 + 273 + 42
    = 171 feet

The height of the rocket after 3 seconds is 171 feet.

What is a function?

A function is defined as a relation between the set of inputs having exactly one output each.

The height = -16t² + 91t + 42

After 3 sec means, t = 3, so we substitute t with 3

In order to find the height of the rocket after t seconds we plugin t = 3 in the function.

height H = -16t² + 91t + 42

H = -16(3)² + 91(3) + 42

   = -144 + 273 + 42

   = 171 feet

Thus, the height of the rocket after 3 seconds = 171 feet.

Learn more about function here:

https://brainly.com/question/2253924

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y+2=−2(x−3)

Slope from equation
Problem
What is the slope of the line?

Answers

y = -2x + 6 - 2
y = -2x + 4
The slope of the line is -2.

Please find below the given equation-

y + 2 = -2 ( x - 3 )

y + 2 = -2 x - 2(- 3)

y + 2 = -2 x + 6

y = -2 x + 6 - 2

y = -2 x + 4

Let's compare this equation with the form y = mx +c

By comparing we get,

m = -2 and c = 4

We know, in y = mx + c , slope of the line is given by m

Here m = -2, as discussed above

Therefore the slope of the given line is -2

Hope it helps ..!!

Solve the following equation. Then place the correct number in the box provided. 9(x - 6) = 8(x + 6)

x=

Answers

Hello!

9(x - 6) = 8(x + 6)

The first step to take here is to apply the Distributive Property, which is
a(b + c) = ab + ac.

9(x - 6) = 8(x + 6)
9x - 54 = 8x + 48

After this, you want to begin to eliminate terms to ultimately isolate x; you can subtract 8x from both sides first:

9x - 54 = 8x + 48
x - 54 = 48

Finally, add 54 to both sides to get x by itself:

x - 54 = 48
x = 102

Answer:
x = 102
The answer is 102.
9(x -6) = 8(x+6)
9x - 54= 8x +48
x- 54= 48
x= 102

NEED HELP PLEASE :) ONLY 100% ANSWERS
1) An Egyptian pyramid has a square base that measures 80 meters on each side. If the height of the pyramid is 30 meters, what is the slant height of the pyramid?

2) A room in a bank is shaped like the rectangular prism shown below. The room has a security system that is triggered by two laser beams which stretch from Point A to D and Point B to C. How many total feet of laser beams are there?


*A 3-D rectangle 15 ft. length the back rectangle 12 ft. width the side 35 ft. width front*

Answers

first answer is 81.39 but can't picture the second one without a figure

Answer:

1)  the slant height of the pyramid is 50 meters.

2) there are (approximately) a total of 80 ft of laser beams.

Step-by-step explanation:

1) The height of the pyramid (30 m) and half of the length of its base (40 m) form a rectangular triangle, where the slant height is its hypotenuse (H). From Pythagorean theorem:

H^2 = 30^2 + 40^2

H = √2500

H = 50 m

2) In the figure attached the rectangular prism is shown (point E was added).

The length of the laser beams is the addition of the segments AD to segment CB (which are equal).

We can make a rectangular triangle between points ECD. From Pythagorean theorem:

ED^2 = EC^2 + CD^2

ED = √(12^2 + 35^2)

ED = 37 ft

We can make a rectangular triangle between points AED. From Pythagorean theorem:

AD^2 = EA^2 + ED^2

AD = √(15^2 + 37^2)

AD ≈ 40

Then, there are (approximately) a total of 80 ft of laser beams.

(4 + y = 19) what is y

Answers

4 + y = 19

y = 19 - 4

y = 15

On a map, 1.5 centimeters represents a distance of 45 kilometers. If two points on the map are 0.8 centimeters apart, what is the actual distance between the two points?

Answers

Write a proportion
centimeters / kilometers
1.5 / 45 = 0.8 / x
cross multiply
(1.5 * x ) = (45 * 0.8)
1.5x = 36
divide both sides by 1.5
x = 24

The actual distance between the two points is 24 kilometers.

Hope this helps

Use the diagram to complete the statement. Given JKL, sin(38) equals—
(Diagram is a right triangle. Angle K is 52 degrees and angle L is 38)

cos(38)
cos(52)
tan(38)
tan(52)

Answers

Cos(52) . Sine and Cosine are cofunctions so to convert from one to the other you subtract the value from 90 to get the other function.  90-38= 52.  you can check this by putting both into a calculator.  (in degree mode on calculator)
sin(38) = 0.61566......
cos(52) = 0.61566......

Answer:

Answer is b

Step-by-step explanation:

Carly has 5 times as many markers as camden.Toegether they have 30 markers.How many markers does Carly have? How many markers does Camden have

Answers

Carly has 5 and Camden has 6

5x6=30

Answer:

number of markers Camden has = [tex]5[/tex]

number of markers Carly has = [tex] 25[/tex]

Step-by-step explanation:

Let the number of markers Camden has = x

now it is given that Carly has 5 times as many markers as Camden has

Number of markers Carly has = 5 ( number of markers Camden has )

                                                   = [tex]5x[/tex]

now the total number of markers = 30

number of markers with Carly + number of markers with Camden = 30

so we have

[tex]5x+x = 30[/tex]

[tex]6x =30[/tex]   ( adding like terms x and 5x)

[tex]x=\frac{30}{6}[/tex] ( dividing both sides by 6)

[tex]x= 5[/tex]

hence we have

number of markers Camden has = [tex]x=5[/tex]

number of markers Carly has = [tex]5x= 5(5) = 25[/tex]

The age of a father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. If the son age is s years, which equation models this situation?

a. (s+3)+[(7s-2)+3}=52
b. 3s+3+3(7s-2)= 52
c. s+(7s-2)=52
d. (s-3)+(7s-2)-3=52

Answers

First,
the age of the son: s
the age of the father is 2 less than 7 times the age of his son: 7s - 2
In 3 years, the sum of their ages will be 52,
In 3 years, the age of the sun will increase 3, so s+3. Also, the age of his father also increase 3, (7s - 2) + 3

(s+3) + [(7s-2) + 3] = 52 is the equation. 

If p(q-r)x^2 +q(r-p)x + r(p-q) has equal roots,then, 2/q=??
a)p+ 1/r c)p+r
b) 1/p +r d) 1/p + 1/r

Answers

The answer is d) 1/p + 1/r.
Solution to this is,
[r(p-q)/p(q-r)]=1
pr-qr=pq-pr
2pr=pq+qr
2pr/pqr=(pq+qr)/pqr
2/q=1/r+1/p

Write an algebraic expression for the verbal description. the sum of two consecutive natural numbers, the first of which is n

Answers

I think it may be:

n + (n + 1)

hope this helps
Two consecutive natural numbers would be 1 and 2, or 5 and 6, for example.

If the first number is n and the second number is n+1, then you are writing [tex]n+(n+1)=2n+1[/tex].

Convert 1/ 3 to a fraction with denominator of 9

Answers

1/3
1 x 3 = 3
3 x 3 = 9
3/9

[tex]\frac{1}{9}[/tex]  is the new fraction after converting or expanding the given fraction [tex]\frac{1}{3}[/tex] with the denominator 9.

Expanding a fraction:

Expanding a fraction means making it "bigger".

How we expand a fraction?

We can expand a fraction by multiplying the numerator and denominator with the same number.

According to the given question we have a fraction [tex]\frac{1}{3}[/tex].

Since, we have to convert or expand the given fraction with the denominator 9.

We know that 3× 3 = 9.

So, multiply the numerator and the denominator of the given fraction by 3.

⇒ [tex]\frac{(1 )(3)}{(3)(3)} = \frac{1}{9}[/tex]

Hence, we have converted  or expanded the fraction [tex]\frac{1}{3}[/tex] with the denominator of 9.

Learn more about expanding the fraction here:

https://brainly.com/question/17991276

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If s = 1 over 3 unit and A = 54s2, what is the value of A, in square units? ____ square units. (Input whole number only.)

Answers

Plug 1/3 in for s. Then multiply 54 by 1/3. Next you multiply that by 2. The answer should be close to 35.999 or 36 square units.

Kohl's sells casual shirts for $9 and polo shirts for $18.00. Total sales were $1,080, and customers bought 4 times as many casual as polo shirts. How many casual shirts did Kohl's sell?
a. 40
b. 12
c. 20
d. 60

Answers

trick question so i believe its 
60 
please correct e if im wrong

which of the following choices describe the bases of a cylinder? check all that apply.
a. discs
b. parallel
c. similar
d. congruent

Answers

Answer:

  all apply

Step-by-step explanation:

All of the given descriptors apply. The bases of a cylinder are congruent parallel discs. Congruent figures are also similar.

Answer:

a,b,d

Step-by-step explanation:

equation that passes through the points (-1,0)(0,2)

Answers

1. Find the slope.

2. Plug the slope you found in step 1, one of the given points, and plug both into the point-slope formula.

The point-slope formula is:

y - y_1 = m(x - x_1)

3. Solve the point-slope formula for y.

Your final answer must be in the form

y = mx + b
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