Mathematics College

The Leibnitz notation for the chain rule is
(1 point) Suppose y = sin(x2 - 4x). We can write y = sin(u), where u =
dy dy du
dy
du
The factors are
(written as a function of u ) and
dx du dx
du
dx
x for u to get
Now substitue in the function of
=
dy
dx
(written as a function of x ).

The Leibnitz Notation For The Chain Rule Is(1 Point) Suppose Y = Sin(x2 - 4x). We Can Write Y = Sin(u),

Answers

Answer 1

For this derivative, you could set

[tex]\boxed{u = x^2 - 4x}[/tex]

Then

[tex]y = \sin(x^2-4x) = \sin(u)[/tex]

so that

[tex]\boxed{\dfrac{\mathrm dy}{\mathrm du} = \cos(u)}[/tex]

and

[tex]\boxed{\dfrac{\mathrm du}{\mathrm dx} = 2x - 4}[/tex]

Then the chain rule gives

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \cos(u)(2x-4) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = (2x-4)\cos(x^2-4x)}[/tex]

Related Questions

2. Read "Lisa's Garden" and answer the question.
Lisa needs to determine the perimeter of her garden so she will know
how much fence she will need to build. What is the perimeter of Lisa's
garden in feet (ft)?
A
30 ft
B
38 ft
C.
120 ft
D
608 ft

Answers

38 Is it explain step by step
D I think if it’s wrong im sorry

PLEASE NO LINKS AND PLEASE HURRY

Answers

Answer: the answer is the last one, 2 and one thirds minus two and two thirds

Step-by-step explanation: free the equation from parentheses by multiplying 1/3 by 5x and 8. equals 5/3x - 8/3 + 2/3. Combine x's for 7/3 - 8/3. Convert into mixed numbers fo final equation

Solve using the square root method X2=25
​

Answers

Answer:

Square root =

remember :

[tex]\boxed {x^2 = \pm a}[/tex]

x² = ± a

x = ña

.

x = ñ25

x = ±5

• x = 5 and -5

x^2=25
sqrt x^2= sqrt 25
x=5

A field hockey field is rectangular. It's width is 54.88 meters and its length is 91.46 meters.find the perimeter of the field

Answers

Answer: 292.68 m²

Step-by-step explanation:P=2a+2b

P=2*54.88m+2*91.46m

P=109.76m+182.92m

P=292.68m²

PLEASE HELP ME, GUYS!

Answers

Answer:

Okay I got youuu

Step-by-step explanation:

From the point Z go 5 right and 3 units up (5,3), and label it Z'. Do this for L and X, too.

The final answer is Z'(2,3) X'(5,0) L'(3,-1)! Hope this helps!

Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

A is the correct answer.

Answer:

A. I believe

Step-by-step explanation:

After 12 years I shall be three times as old as I was 34years ago. Determine my present age

Answers

Answer:

the 34 yrs Is wrong it will be 4yrs only.

Step-by-step explanation:

Let my present age=x years

After 12 years my age=x+12 years

4 years ago my age =x−4 years

According to the question,

x+12=3(x−4)

⇒x+12=3x−12

⇒3x−x=12+12

⇒2x=24

or x= 24/2 =12 years.

∴ my present age is 12 years.

hope this helps you.

Let the present age of let’s say todd be X

Todd’s age (x+12) will be 3 times as old as he was 4 years ago [3(x-4)]

i.e



x+12=3(x-4)
x+12=3x-12

2x=24
X=12.
Hence Todd’s present age is 12.


find the average rate of change of f(x)=5x^2-3 from 3 to 9

Answers

9514 1404 393

Answer:

  60

Step-by-step explanation:

The average rate of change on the interval is ...

  (f(9) -f(3))/(9 -3) = ((5·9² -3) -(5·3² -3))/(9 -3) = (402 -42)/6 = 60

The Parker company employs 68 part time workers. If this represents 4% of the total work force, how many individuals work for the company?

Answers

Answer: ite will be 3 bc i done that all ready

Step-by-step explanation:

The number of individuals that work for the company is 272 workers.

Given,

The Parker company employs 68 part-time workers.

This represents 4% of the total workforce.

We need to find out how many individuals work for the company.

What is percentage?

Percentage is a fraction or a ratio in which the value of whole is always 100.

Find the total workforce.

Total workforce = 100%

We have,

4% = 68 workers

Multiply 25 on both sides.

25 x 4% = 4 x 68 workers

100% = 272 workers.

This means the number of individuals that work for the company is 272 workers.

Thus the number of individuals that work for the company is 272 workers.

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Y=arccos(1/x)

Please help me do them all! I don’t know derivatives :(

Answers

Answer:

Step-by-step explanation:

A box is in the shape of a triangular prism. . The base of the triangular face of the box is 11 centimeters (cm). The height of the triangular face of the box is 7.5 cm. The length of the box is 15 cm. V =1/2hxbxl What is the volume of the box? A 277.5 cm B 577.5 cm C 618.75 cm D1237.5 cm
​

Answers

Answer:

[tex]618.75 cm^{3}[/tex]

Step-by-step explanation:

[tex]\frac{(11 cm)(7.5 cm)(15 cm)}{2} =618.75 cm^{3}[/tex]

Which data set has the same standard deviation as the data set {2,2,5,6,8}?

A. {3,4,4,7,7}
B.{5,6,5,6,5}
C.{3,3,6,7,9}
D.{4,4,5,5,5}

Answers

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

A bank randomly surveyed 50 of its customers by mail to find out how customers use its mobile banking service. The survey found that only 11 of the 50 customers used the service.

If the branch has 1,700 customers, about
customers use the mobile banking service.

Answers

22 percent of the costumers used the service

and 78 percent didnt

Answer:

374

Step-by-step explanation:

x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³x³+y³+z³ [tex]x³+y³+z³[/tex]

Answers

This equation is in wrong format

Can someone help……….

Answers

Answer: There are no outliers

Y=5x-13
Y-intercept
X-intercept

Answers

Answer: The internet solve it for me.

Step-by-step explanation: To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

3x-47=180 solve for x

Answers

Answer:

x=75.66

Step-by-step explanation:

+47  180+47

3x=227

divide 3 on each side

x=75.66

3x-47=180

add 47 to both sides

3x=227

divide by 3

x= 75 2/3

You’re recording inventory after a big weekend sale in the travel section of a department store. There are 20 remaining suitcases, of which 16 will be further marked down. True or False: The fraction 2016
20
16
is in the simplest form.

Answers

Answer:

false

Step-by-step explanation:

Given that the remaining suitcases is 20

And 16 of the remainig suitcases will be further marked down, then the simplest form will be;

16/20.

7
Compare the fractions
3
64
8
A)
<
B)
C)

Answers

Answer:

74/8

Step-by-step explanation:

Answer:

LCM of 64 and 8 is 64

Step-by-step explanation:

Ryan has a bank account balance of −$17.62. As soon as he realizes this, he deposits $26.50 in the account.

What is Ryan's bank account balance after the deposit is made?

Enter your answer in the box.

$

Answers

Answer:

$466.93

Step-by-step explanation:

I multiplied by 26.50 & 17.62 and that got me $466.93. Or you can divide that into 17.62 = $1.50

Kelly tried to solve the following equation,

Answers

Answer:

wich question??????????????

cual

no te entiendo me puedes explicar

help pls. with explanation

Answers

Answer:

the answer is infinity....

Abigail is trying to rent a boat while on vacation. She has two options to choose from.



Bruce's Boats: $22.50 per hour plus a one time fee of $85


Peter's Pontoons: $65.00 per hour


After how many hours, will Bruce's Boats, and Peter's Pontoons charge the same amount?

A.130
B.2
C.3
D.85
ANSWER QUICK

Answers

Step-by-step explanation:

D bruce's boats: $22.50

A
,
B
and
C
form a triangle where
∠
B
A
C
=
90
∘
.
A
B
=
12.1
mm and
B
C
=
19.7
mm.
Find the length of
A
C
, giving your answer rounded to 1 decimal place.

Answers

Answer:

15.5 mm

Step-by-step explanation:

Given:

ΔABC with ∠BAC = 90°, AB = 12.1 mm, BC = 19.7 mm

Since BC is opposite to right angle, AC is the missing leg.

Find AC using Pythagorean:

[tex]AC = \sqrt{BC^2-AB^2} =\sqrt{19.7^2-12.1^2} =\sqrt{241.68} =15.5 mm[/tex]

Mr. Adkins teaches a Current Events course and is known for making his final exam very thorough. He thinks that with the technology present today,
his students should be able to stay current with all possible news. The only way to ensure yourself a good grade is to dedicate many hours reading
newspapers, watching 24 hour news outlets, and scanning the internet, and even that may not give you the desired test score. Adkins' students
kept track of the hours that they studied the week previous to the test. Here is a breakdown of the hours that they studied and the score they
received on the test.

Answers

Answer:

Part 1:

Make a scatterplot that represents this data. You may use a program such as Excel, or make the scatterplot by hand and scan it.

Part 2:

Does this data have a positive correlation, negative correlation, or no correlation?

Part 3:

Without the use of technology, find the equation of the line of best fit for the data. Tell which points that you used and show the steps you used to get the equation. Refer to the first 4 steps on page 2 of the lesson titled "Linear Regression - Line of Best Fit" to use as a guide.

Part 4:

Use the equation found in part 3 to predict the scores for two people who studied for 15 hours and 9 hours. Refer to the last step on page 2 of the lesson titled "Linear Regression - Line of Best Fit" to use as a guide.

Compile the results from parts 1 through 4 and put them in a Word document. Submit the document to your teacher.

Step-by-step explanation: help

27. Representative Sample? You want to determine the average number of classes skipped by
first-year students at a small college during a particular semester. State whether each of the
following samples is likely to be representative and explain why or why not.
Sample 1: 100 first-year students who belong to a sorority or fraternity
Sample 2: 100 first-year students who play a varsity sport
Sample 3: The first 100 first-year students whom you meet at the student union
Sample 4: 100 first-year students taking honors humanities,, courses

Answers

A sample is said to be representative if the selection made form have population is free of bias. Evaluating the selection criteria listed above :

Sample 1 will not likely be representative as students who do not belong to either a sorority or fraternity are automatically exempted from the selection.

Sample 2 will not likely be representative because not all students play a varsity sport, hence students who do not play a varsity sport won't have a chance of being selected.

Sample 3 is a convenience sampling technique, they often exhibit sampling bias hence, sample 3 is not representative of the population.

Sample 4 will not likely be representative as students taking other courses aside humanities have no chance of being selected.

Therefore, all the sampling methods are not representative of the population of first year student.

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An online school with 125 classes has a student enrollment of 2,500 students. Which rate represents the relationship between the student enrollment and the number of classes? 12 classes per student 20 classes per student 20 students per class 30 students per class

Answers

Answer 20 classes per student

Step-by-step explanation:

This is worth 30 points I need help ASAP PLEASE PLEASE HELP!!

Answers

Answer:

c

Step-by-step explanation:

smart boi

Step-by-step explanation:

A = (3, 6)

B = (6, 9)

C = (9, 3)

first scaled down (dilated) by the factor of 1/3 in the direction of the origin = point (0, 0).

then moved left by 2 units and down by 3 units.

the dilation about the origin simply multiplies each coordinate by the scale factor.

Ad = (3×1/3, 6×1/3) = (1, 2)

Bd = (6×1/3, 9×1/3) = (2, 3)

Cd = (9×1/3, 3×1/3) = (3, 1)

to move 2 units to the left means to subtract 2 from the x coordinates.

to move 3 units down means to subtract 3 from the y coordinates.

A' = (1-2, 2-3) = (-1, -1)

B' = (2-2, 3-3) = (0, 0)

C' = (3-2, 1-3) = (1, -2)

therefore, B is the right answer option.

round 0.25 to the nearest hundredth ​

Answers

Answer:

0.25

Step-by-step explanation:

there is no hundredth in 0.25

Rounding 0.25 to the nearest hundredth gives us 0.26.

We must look at the digit in the thousandth place, which is the following decimal place after the hundredth place, in order to round 0.25 to the closest hundredth.

We round up the digit in the hundredth place by adding 1 since the digit in the thousandth place is 5, which is equal to or larger than 5.

Thus, 0.26 is obtained by rounding 0.25 to the next tenth.

0.25 (initial number) worked

(Number in the thousandth place) (Number in the hundredth position)

We round up the digit in the hundredth place since the digit in the thousandth place is 5, which is 5.

Hence rounding to the nearest hundredth, 0.25 equals 0.26.

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HELP PLEAASEEEE pretty anyone

Answers

Answer: It's the third one

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's A.

1/5k is greater than 0 if k > 0

-2/3 j is less that 0 if j >0

When you look at the second half of this, what has happened is that - 2/3 is written first and it is still minus. 1/5 k is plus just as it was before.

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