y equals the quotient of the quantity x squared plus 4 times x and the quantity x cubed minus 5.

Answers

Answer 1

Given:

Consider the completer question is "Find the derivative [tex]\dfrac{dy}{dx}[/tex] for [tex]y=\dfrac{x^2-4x}{x^3-5}[/tex]."

To find:

The derivative [tex]\dfrac{dy}{dx}[/tex].

Solution:

Chain rule: [tex]\dfrac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)[/tex]

Quotient rule: [tex]\dfrac{d}{dx}\dfrac{f(x)}{g(x)}=\dfrac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]

We have,

[tex]y=\dfrac{x^2-4x}{x^3-5}[/tex]

Differentiate with respect to x.

[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{x^2-4x}{x^3-5}\right)[/tex]

Using chain rule and quotient rule, we get

[tex]\dfrac{dy}{dx}=\dfrac{(x^3-5)\dfrac{d}{dx}(x^2-4x)-(x^2-4x)\dfrac{d}{dx}(x^3-5)}{(x^3-5)^2}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{(x^3-5)(2x-4)-(x^2-4x)(3x^2)}{(x^3-5)^2}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{2x^4-4x^3-10x+20-3x^4+12x^3}{(x^3-5)^2}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}[/tex]

Therefore, the required answer is [tex]\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}[/tex].


Related Questions

determine the equation of the line

Answers

Answer:

y=5x-12

Step-by-step explanation:

the slope is 5 and y int. is -12

Savannah and Reagan both work in a grocery store. They each stocked the same number of shelves last Saturday, but it took Reagan less time. They've been told that they'll spend their entire 4-hour shifts next Saturday stocking shelves. If their average speeds are consistent, who will likely stock more shelves next Saturday?

HELP!

Answers

Answer:

Reagan

Explanation:

Since Reagan is able to stock the same number of shelves as Savannah while spending less time to do so, it means that Reagan is able to stock shelves faster than Savannah, thus Reagan is able to stock more shelves than Savannah given that their average speeds are constant and that they both work under 4-hour shifts.

Hope this helps :)

what is the cost of 1 pound of pears?

Answers

Answer:

2.8

Step-by-step explanation:

Answer:

$1.75

Step-by-step explanation:

could somebody help please

Answers

if you have zero dollars you can’t buy anything

I Need Help ASAP!!!​

Answers

Answer:f(x) in order from left to right= -20, 5, 10, 15, 30 i.) -.06 ii.)-40

Step-by-step explanation: f(x) is the answer of 5 times whatever x is, so when it’s telling you what x is all you have to is multiply it by the number next to x which in this case is 5. after doing that you get the answers above. for i.) it’s telling you the answer which is -3, so you divide that by 5 getting -.06. In ii.) it gives you x which is -8 so you plug that in giving you -40.

If 7 pounds cost $5.46, find the cost of 3 pounds. ​

Answers

Answer:

$2.19

Step-by-step explanation:

7 divided by 3 is 2.5

5.46 divided by 2.5 is 2.184

round it and get 2.19

Solve the equation sin^2x=3Cos^2X.

I would love to graduate...so thanks in advance!

Answers

Answer:

240°

Step-by-step explanation:

[tex]sin^2x=3cos^2x \\ \\ sin^2x=3(1 - sin^2x )\\ \\ sin^2x=3 - 3sin^2x \\ \\ sin^2x + 3sin^2x=3 \\ \\ 4sin^2x=3 \\ \\ sin^2x= \frac{3}{4} \\ \\ sinx= \sqrt{ \frac{3}{4} } \\ \\ sinx= \frac{ \sqrt{3} }{2} \\ \\ sinx= sin \: 60 \degree \\ \\ in \: the \: second \: quadrant \\ sinx= sin \: (180 \degree - 60 \degree ) = sin \: 120 \degree \\ \\ in \: the \: third \: quadrant \\ sin x= sin \: (180 \degree + 60) \degree = sin \: 240 \degree[/tex]

the green shape is a dilation of the black shape.what is the scale factor of the dilation? ​

Answers

Answer:  5

Step-by-step explanation:

Scale factor = [tex]\dfrac{\text{ side length of image}}{\text{Side-length of original figure}}[/tex]

Given: Black triangle ( original) having perpendicular with length 4 units.  [2 blocks above and 2 boxes below the x-axis ]

Green triangle ( image) having corresponding side as 20 units  [10 blocks above and 10 boxes below the x-axis ].

Scale factor of dilation = [tex]\dfrac{20}{4}=5[/tex]

Hence, the scale factor of the dilation = 5

geometry help please :)

Answers

Answer:

Medium to Line AC

Altitude to Line AC

Bisector of Angle B

Perpendicular bisector of Line AC

Step-by-step explanation:

We can tell that the Medium here is from line AC to angle B. The line is connecting the angle to the middle of the line, making it the medium and altitude. It is also a bisector of angle B because it is directly in the middle of that angle. It is a perpendicular bisector to line AC because it forms a 90 degree angle on the bottom.

#teamtrees #WAP (Water And Plant)

Mrs Jonas has 35 students in her math class. If her class increases to 42 students next year what will be the percent of change?

A) 335

B) 93%

C) 75%

D) 20%

Answers

Answer:

D. because I did it

Step-by-step explanation:

got it right.

Answer:

20%

Step-by-step explanation:

well if the class would increase 35+35 it would be 50 % so its supposed to be a smaller percentage

To measure the length of the pond, Jacob marked off congruent triangles as shown in the diagram.

How does he know the lengths of AB and XY are equal?

A. AAS and then corresponding parts of congruent triangles are congruent

B. SSS and then corresponding parts of congruent triangles are congruent

C. SAS and then corresponding parts of congruent triangles are congruent

D. ASA and then corresponding parts of congruent triangles are congruent

Answers

Answer:

B

Step-by-step explanation:

whats one plus 1 x 111111100000+y7897654323456x1

Answers

Answer:

Shoyo here!

Step-by-step explanation:

10000000000000000000000000000000

What is the constant of proportionality in the equation y=0.72x

Answers

Answer:

Constant: 0.72 = 18 : 25

Step-by-step explanation:

None

*show all work for full credit
1. 6x=25

Answers

6x=25
we need to divide by 6 on both sides so we will get:
6x/6=25/6
after doing this we will get:
x=25/6
depending on what your teacher is asking for, 25/6 will be your answer or your answer will be 4.16.

Answer and Step-by-step explanation:

All we have to do is solve for x.

Divide both sides by 6.

x = [tex]\frac{25}{6}[/tex]

This is your answer.

If you want to have the decimal version, then it would be 4.166 repeating.

#teamtrees #WAP (Water And Plant) #SPEW (Society for the Promotion of Elfish Welfare)

Choose the situation in which the use of approximate numbers is most appropriate.
A)
planting trees in your yard
B)
ordering chairs for a kitchen table
purchasing barbeque to serve at a party
D
ordering uniforms for the high school basketbalt team

Answers

I good with D because i think it’s for Sure the right answer

Answer:

I would say that A  is your answer.

I think this because you would not need to have any specific number of trees in your yard, but you would need a specific number of things for all of your other options.

Step-by-step explanation:

You probably wouldn't approximate on how many chairs you put in a kitchen. What if you have a 5-member family and you aproxomate the chair number to 4. that would be useless so B is wrong.

C is wrong because you are only getting 1 barbaque. no approximation is nessisary for one item.

D is certainly wrong because you wouldn't want to leave out a uniform, that would mean one member of the basketball team may not get one.

A particle is moving along the number line so that its distance (in meters) from the origin at any time t (in seconds) is given by s(t) = 8t2 + ln t.

The velocity of the particle at t = 1 second is:

Answers

Answer:

The velocity is 17 m/s

Step-by-step explanation:

To find the velocity, we find the first differential of the displacement

That will be

S’(t) = 16t + 1/t

We simply proceed to replace t with 1

That will give;

16(1) + 1/1

= 16 + 1 = 17 m/s

The scatter plot shows the amount of sleep Aria got the night before a test and her test scores. Which is the best prediction for Aria’s grade when she sleeps for 10 hours?

A 75
b 83
C 92
D 99

Answers

Answer: y= 3x+62

Step-by-step explanation: m= y₂-y₁/x₂-x₁

m= 80-62/6-0

m= 18/6

m=3

y-y₁=m(x-x₁)

y-62= 3(x-0)

y-62= 3x-0

y= 3x+62

There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows. How many possible ways can the chairs be lined up

Answers

Answer:

2 rows of 41

Step-by-step explanation:

i had the same question

The number of possible ways can the chairs be lined up is 2 rows of 41.

Given that,

There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows.

Based on the above information, the calculation is as follows:

[tex]= 2 \times 41[/tex]

= 82 chairs

Here 2 denotes the rows.

Therefore we can conclude that the number of possible ways can the chairs be lined up is 2 rows of 41.

Learn more: brainly.com/question/13549064

If the price of beef rose from $8.72 per pound to $9.43 per pound, what is the percent of increase? Round to the nearest percent

Answers

Answer:

8.1%

Step-by-step explanation:

Step one:

given

initial price = $8.72 per pound

final price=  $9.43 per pound

Required

the % increase

Step two:

% increase= (final-initial)/initial*100

substituting we have

[tex]percent- increase= (9.43-8.72)/8.72*100\\\\percent- increase= 0.71/8.72*100\\\\percent- increase= 0.081*100\\\\percent- increase= 8.1%[/tex]

A spinner can land on either red, blue, green, or yellow. You spin once.
Find the number of possible outcomes in the sample space.
Please show me how to solve this.

Answers

Answer:

You have a 25% chance on landing on any of the colors  

Step-by-step explanation:

You Look at all of the posible ways you can land on which is Red, Blue, Green, and Yellow there are four colors in the spinner if you divide the number of colors (4) and divide it by 100 you will get 25 and that is your answer

Considering it's concept, it is found that the number of outcomes in the sample space is of 25%. You have a 25% chance on landing on any of the colors  

What is the sample space of an experiment?

The sample space is the set that contains all possible outcomes for an experiment.

here, we have,

In this problem,

You Look at all of the possible ways you can land on which is Red, Blue, Green, and Yellow

there are four colors in the spinner

if you divide the number of colors (4) and divide it by 100

you will get 25 and that is your answer

Hence, Considering it's concept, it is found that the number of outcomes in the sample space is of 25%. You have a 25% chance on landing on any of the colors.

More can be learned about sample spaces at brainly.com/question/25861936

#SPJ3

please help me answer this ASAP if u view it then u'll see the question properly
[tex] \frac{1 + \sqrt{3} }{ \sqrt{12} } [/tex]
i will give brainliest answer if it the correct answers ​

Answers

Answer:

1/6 sqrt(3) + 1/2

Step-by-step explanation:

(1 + sqrt(3))

------------------

sqrt(12)

Multiply the top and bottom by sqrt(12)

(1 + sqrt(3)) * sqrt(12)

------------------

sqrt(12)*sqrt(12)

sqrt(12) + sqrt(3) * sqrt(12)

------------------

12

Simplify

sqrt(4)sqrt(3) + 6

------------------------

12

2 sqrt(3) +6

--------------------

12

1/6 sqrt(3) + 1/2

Please help me on this

Answers

Answer:

PAGE 1

8.) d

9.) b

PAGE 2

6.) b

7.) d

PAGE 3

4.) c

5.) a

PAGE 4

1.) c

2.) c

3.) a

PAGE 5

10.) b

11.) d

Step-by-step explanation:

PAGE 1

8.) x - 20 + x + 10 = 180 (collect like terms)

2x - 10 = 180 (add 10 on both sides)

2x = 190 (divide by 2 on both sides)

x = 95

9.) 2y + y = 180 (collect like terms)

3y = 180 (divide by 3 on both sides)

y = 60

x = y ----> x = 60

PAGE 2

6.)  16x - 6 = 90 (add 6 on both sides)

16x = 96 (divide by 16 on both sides)

x = 6

7.) 5x + 30 = 7x (subtract 5x on both sides)

30 = 2x (divide by 2 on both sides)

15 = x

PAGE 3

4.) <8 and <16 are corresponding angles

5.) 180 - 130 = 50

PAGE 4

1.)  HD and GE are skew lines

2.) AC, EG, and BD are parallel to FH

3.) EF, GH, and BF are perpendicular to FH

PAGE 5

10.) | and || only are the only ones correct

11.) l || m, by the Converse of the Consecutive Interior Angles Theorem.

b/c the two angles equal 180 together and one angle is on line l and the other is on line m. This shows they're parallel.

Hope this helps ya!!

The regular price is $8.45 more than the sale price. The regular price
is $24.95. What is the sale price? _____

Answers

Answer:

33.04

Step-by-step explanation:

just add lolz :P

Answer:

$33.40

Step-by-step explanation:

  1  1  1

  24.95

+   8.45

__________

    33.40

5+5 is 10 so bring a 1 to the top and put a 0 for the bottom

1+9+4 is 14 so put the 4 down and put the 1 on top.

1+4+8 is 13 so put the 3 down and put the 1 on top.

1+2 is 3 so put the 3 down

then you get 33.40

Question 6: please help me out here :(((

Answers

Answer:

m∠1 = 106

Step-by-step explanation:

Given: m∠5 = 106

Vertical angles are congruent

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.

Therefore: m∠1 = 106

y−4=7(x−6) what is the ordered pair solution for this problem

Answers

This is your perfect answer

4. write the following in standard form
four hundred, thirty - two thousand, six hundred eight

Answers

The answer is 432,608

What is 16 x 2? This is a random question! I want to give away points so be quickkkkk!

Choose
A) 31
B) 34
C) 32
D) chicken wing

Answers

Answer: C.)32 Bestieeeee

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Help me on this please

Answers

Answer:

A. x1/15

Step-by-step explanation:

Answer:

It would be [tex]x^{\frac{8}{15}}[/tex] or D

Hope this helps

how many times does 50 go into 102?​

Answers

2 because 50 x 2 is 102

Answer: 2 times with a remainder of 2. Remainder basically means whats left over and in this case, it's 2

Step-by-step explanation: 2 times 50= 100

If sally has 10 lollipops and gives 3 away but then but 14 more and eats 3
how many lollipops does sally have? If it is correct you can get points and brainilist

A) 13
B) 3
C) 20
D) 18

Answers

Answer:

D) 18!

Step-by-step explanation:

HAHAHAHAHH BESTIEE

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