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 ).

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]

A rectangular prism with a square base has height 12 ft. The volume of the prism is 3468 cubic feet. Determine the side length of the base of the prism to the nearest foot?? what is the answer to this

Dr. Seals borrows $15,000 to remodel her backyard. The interest rate is 3%. The interest is compounded twice a year for two years.

HELP!!! Name the space figure you can form from the net.

hi can you please help me with my work​ please no Link please no Link

Huiling bought 18 chicken nuggets.
She ate 6 of them.
What fraction of the chicken nuggets did she eat?
Give your answer in its simplest form.​

the age of three sibling leon,kelly,and jack are in the ratio 3: 5: 6:. the sum of their age is 42 years.how old is kelly?​

in a field
number of sheep : number of cows = 10:3
Zak says,
"There are 10 sheep in the field."
Give a reason why Zak could be wrong.

What is the missing value?
54
30%
100%
?

Which of the statements is false about the additive identity?
A. if y is the additive identity, then x+y=x
B. the value of the additive identity is 0
C. Adding the additive identity corresponds to making no movements at all on the number line
D. it is the number you add to another number to get 0

the equation for this line of best fit is shown below, where d is the distance in miles and f is the fare in dollars.

f = 0.1d + 100



Which of these is a correct interpretation of the slope of this line?



A.
The fare increases $10 for every additional mile

B.
The fare increases $0.10 for every additional 100 miles

C.
The fare increase $0.10 for every additional mile

The angles below are complementary. Find the value of X​

In a rectangular prism, given a base area of 64 cm2 and a
height of 7.2 cm, what would be the volume of the
figure?

Given X=[b a 4 a], Y=[c d a b], and Z=[a c 16 b]. What is Y if x-2y=z?

Each week, the Pickering Trucking Company randomly selects one of its 30 employees to take a drug test. Write an application that determines which employee will be selected each week for the next 52 weeks. Use the Math.random() function explained in Appendix D to generate an employee number between 1 and 30; you use a statement similar to:

GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)

If y = 4x, x = 2z, and z = 3a, what is the value of y - x in terms of a?
A) -20a
B) -18a
C) 6a
D) 18a
E) 20a
With steps please

Each student in Mr.Carey’s class donated 15$ to a charity. There are 24 students in the class which expression could have been used to calculate the total amount donated?

Workers at the Pythagorean Construction Company are building a new house. They need to make sure that proper right triangles are formed to ensure that a safe house is built. What statement should the builders use to ensure that right triangles are formed? If the sum of the two shorter sides equals the longest side, then the triangle is a right triangle. If the sum of the squares of the two longer sides equals the square of the shortest side, then the triangle is a right triangle. If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle. If the difference of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

Which is typically the only way to purchase a car and receive

a warranty? a. Dealership

b. Auction

c. Used Car lot d. Private Seller.

Six pounds of strawberries cost $11.94. Determine the unit rate and use it to find the price of eight pounds of strawberries.

Could I get some help here
I literally have the iq of a 2nd grader

Need help fast please

Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of information does he need to determine the confidence interval?

A.
the critical value
B.
the number of favorable responses
C.
the standard error of the mean
D.
the standard deviation

Which of the following represents the factorization of the binomial below?
81x2 – 25y2
A. (9x - 5y)(9x - 5y)
B. (9x - 5y)(9x + 5y)
C. (9x - y)(x + 5y)
D. (9x + 5y)(9x + 5y)

Find the measure of <5.
45 = [?]
69%
25

What ions combine together to form
water in a neutralization reaction?

Room's volume is 600 m^3. There is 800 ppm (parts per million) of CO2 in the room.
Fresh air, with the CO2 concentration of 400 ppm starts flowing into the room at the rate of 40 m^3/min. The pressure in the room is constant, so an equal amount of stale air flows out as fresh air flows in, and the CO2 is evenly distributed.
a) Form the differential equation for the amount of CO2 in the room.
b) Solve this differential equation
c) What is the CO2 concentration of the room after fresh air has been flowing in for 30 minutes?

Can someone help me plsssss I’ve been struggling

What is the original price of a pair of shoes if there is a 5% discount and the sale price is $47.03?

PLS HELP THIS IS DUE IN AN HOURRRR