differentiate the following functions (x^3+1)(x-2)÷x^2​

Answers

Answer 1

Given:

The given function is:

[tex]\dfrac{(x^3+1)(x-2)}{x^2}[/tex]

To find:

The differentiation of the given function.

Solution:

Consider the given function,

[tex]y=\dfrac{(x^3+1)(x-2)}{x^2}[/tex]

It can be written as:

[tex]y=\dfrac{(x^3)(x)+(x^3)(-2)+(1)(x)+(1)(-2)}{x^2}[/tex]

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

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

[tex]y=x^2-2x+\dfrac{1}{x}-\dfrac{2}{x^2}[/tex]

Differentiate with respect to x.

[tex]y'=\dfrac{d}{dx}(x^2)-\dfrac{d}{dx}(2x)+\dfrac{d}{dx}(x^{-1})-\dfrac{d}{dx}\2(x^{-2})[/tex]

[tex]y'=2x-2(1)+(-x^{-2})-2(-2x^{-3})[/tex]

[tex]y'=2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}[/tex]  

Therefore, the differentiation of the given function is [tex]2x-2-\dfrac{1}{x^2}+\dfrac{4}{x^3}[/tex].


Related Questions

9.4 ÷ 20
SHEEEEEEEEEEEEEEEESH

Answers

Answer:

[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]

[tex]9.4 \div 20 \\ = 0.47[/tex]

how do I do this? I'm confused.​

Answers

Step-by-step explanation:

[tex]\huge\mathcal\blue{here's \: your \: solution} \\ \\ x = 2y - 14 \: \: \: (given) \\ \\ equation \: = 5x - 7y = - 43 \\ \\ now \: put \: the \: value \: of \: x \: in \: equation \\ \\ 5(2y - 14) - 7y = - 43 \\ \\ 10y - 70 - 7y = - 43 \\ \\ 3y - 70 = - 43 \\ \\ 3y = + 70 - 43 \\ \\ 3y = 27 \\ \\ y = 27 \div 3 \\ \\ y = 9 \\ \\ now \: put \: the \: value \: of \: y \: in \: equation \\ \\ x = (9 \times 2) - 14 \\ \\ x = 18 - 14 \\ \\ x = 4 \\ \\ \huge\mathfrak\red{hope \: it \: helps..}[/tex]

IF YOU ANSWER THESE TWO I'LL GIVE BRAINLIEST (if you only answer one no brainliest)

Answers

The clock one is 20 because there are 4 weeks past and you would just plug that into the equation. The catering one is 118 , also plugging into the equation given.

Answer:

The first question provided (question 11)

The answer is $118.00

The second question provided (question 12)

The answer is 20 seconds

Step-by-step explanation:

The first question provided (question 11)

The equation 5a + 3c is provided to determine the cost of a catering event, where a is the number of adults and c is the number of children.

It is stated that there are 17 adults and 11 children attending an event.

You can substitute in the 17 adults in place of a and the 11 children in place of c.

This will leave you with 5(17) + 3(11).

If you simplify you will get 85 + 33, which is equal to 118

Therefore, the answer is $118.00.

The second question provided (question 12)

The equation s = 5w is provided to determine how far behind a clock is after a certain amount of time, where s is seconds behind and w is the number of weeks sice the clock was last set.

You are given the clock was set 4 weeks ago.

You can subsitute the 4 weeks into the equation in place of variable w.

This leaves you with s = 5(4).

Simplifying this further, you will get s = 20.

Therefore, the clock is 20 seconds behind.

2-3 (8.5A) Hikaru is going to make x pies, he will put 3 pounds of berries in each one, which equation can be used to find b, the total number of pounds
of berries he will put in the pies
A
C b=x+3
5
8
b=x+3
35
b = x - 3
5
B
D
5
b = 3

Answers

Answer:

D

Step-by-step explanation:

the answer is d because it's the 3 and 5/8ths per pie this it is multiplied by x.

The zoo charges $4 admission fee
along with a $2 charge for each
exhibit you visit. what is the initial value, rate of change, and table values

Answers

Answer:

Intial Value; $4 (charged)

Rate of change: $2 every exhibit visited

Admission: $4

1 exhibit visited: $6

2 exhibits visited: $8

3 exhibits visited: $10

4 exhibits visited: $12

5 exhibits visited: $14

6 exhibits visited: $16

7 exhibits visited: $18

8 exhibits visited: $20

etc.

Step-by-step explanation:

4+2x = C

C= Cost

X = amount of exhibits visited

To find the total cost.

Hi, thank you for helping people, have a good day/evening/night.

Answers

Answer:

thx you too

Step-by-step explanation:

Thank you and you’re welcome

I will mark you brainliest if correct

Answers

Answer:

i think its 8.2

Step-by-step explanation:

What is sec 0 when cot 0 = -4V2? 0 (1,0) [?] [ ] Rationalize the denominator if necessary. sec 0 =​

Answers

Answer:

[tex]Sec~ 0=\frac{\sqrt{66} }{8}[/tex]

Step-by-step explanation:

[tex]Cot~0=-4\sqrt{2}[/tex]

[tex]Sec~0=\sqrt{33}/4\sqrt{2}[/tex]

[tex]=\sqrt{33}/4\sqrt{2} *4\sqrt{2} /4\sqrt{2}[/tex]

[tex]=4\sqrt{66} /32[/tex]

[tex]= \sqrt{66}/8[/tex]

᪥༄᪥༄᪥༄᪥༄᪥༄᪥༄

hope it helps...

have a great day!!!

Nadia compares the weights, in grams, of some apples and oranges she find the median abs interquartile range of the weights.

Answers

Answer:

Apple

Orange

Step-by-step explanation:

Apple has the greater median with a median value of 150 which is more than that of orange at 130

The sample with the greater variability is the orange sample as the interquartile range value of 11 is greater Than 8 for Apple.

Yes it is possible, because of the greater variation on weight shown by the sample of oranges, then it could be possible.

Find the lines of symmetry for each shape. Select all that apply.​

Answers

Answer:

It is T and R

Step-by-step explanation:

evauate the problem 5y=30

Answers

Answer:

y = 6

Step-by-step explanation:

5y = 30

5y ÷ 5 = 30 ÷ 5

y = 6

Y=6
5x6=30

Hope this helped

Help asap please I really need it!

Answers

Answer:

[tex]volume = \frac{4}{3} \pi r^3\\\\Radius = 2 , volume = \frac{32\pi }{3}cm^3 \\\\Radius = 3, volume = 36\pi cm^3 \\\\Radius = 4, volume = \frac{256\pi }{3} cm^3\\\\Radius= 6, volume = 288\pi cm^3[/tex]

solve for the value of k

Answers

Answer:

k = 42

Step-by-step explanation:

This is a complementary angle, meaning that the angles formed equal 90 degrees. We know it is complementary because the angle is shown was a tiny square, a sign that it is 90 degrees. Thus, the two angles (k+1) and 47 added together must equal 90. So, we can write an equation:

(k+1) + 47 = 90

k + 1 = 43

k = 42.

K=42
So (42+1)=43 2*43=86 (86+4)=90
I think so thanks

Please I need help!!!!

Answers

Answer:

(9-7)

Step-by-step explanation:

1st

Vertex

we have

f(x)=x²-18x+88

let

y=x²-18x+88

comparing above equation with ax²+bx+c

we get

a=1

b=-18

c=88

now

vertex(x,y)=(-b/2a,f(-b/2a))

x=(18/2×1)=9

y=f(9)=9²-18×9+88=7

SO

VERTEX(X,Y)=(9,7)

Solve the equation below for x.

9(x - 5) = 4x - 5

Answers

Answer: look at the picture

Step-by-step explanation: Hope this help :D

PLS HELP i have to finish this tonight

Answers

Answer:

D.480 Ft/S

Step-by-step explanation:

um, Just ask your teacher if you don't understand:P

What is -29=9-6k-2k-14 If you don't know do not answer!!!
MUST SHOW WORK!!!

Answers

Answer:

Positive 3

Step-by-step explanation:

-29=9-6k-2k-14

-29=-5-8k

-24=-8k

k=3

What is the average of these three numbers?

4,293 4,216 4,304​

Answers

4292+4216+4304=12813
12813÷3=4271


Answer: 4271

how do i do this? please help with answer and explanation

Answers

Answer:

x=7

Step-by-step explanation:

180=25x+5

175=25x

7=x

Answer:

x = 7

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

We know that,

→ Sum of all angles in a line is 180°.

Forming the equation,

→ (13x + 2) + (12x + 3) = 180°

Then the value of x will be,

→ (13x + 2) + (12x + 3) = 180°

→ 13x + 2 + 12x + 3 = 180°

→ (13x + 12x) + (2 + 3) = 180°

→ 25x + 5 = 180°

→ 25x = 180 - 5

→ 25x = 175

→ x = 175/25

→ [ x = 7 ]

Hence, the value of x is 7.

Carla and Deserea bought a dozen cookies from the bakery. Carla ate ¼ of the cookies and Deserea ate ½ of the cookies. Who ate the most

Answers

Answer:

The answer is Deserea.

Step-by-step explanation:

Dont worry, this is simple :)

If you have a dozen cookies, that means you have 12 cookies!

And 1/4 of 12 is simply 12 divided by 4, which equeals 3, so Carla ate 3 cookies.

And Deserea ate ½ of the cookies, which is 12 divided by 2, which is 6! So Deserea ate 6 cookies.

6 is greater than 3. So Deserea ate more Cookies!

Hope this helps!

Deserea Ate the most because 1/2 is a lot more than 1/4. Hope this helps :-)

WILL GIVE BRAINLIEST!!!!
Solve the inequality:

n - 48 < 12

Answers

Answer: n < 60

Step-by-step explanation:

n - 48 < 12

n - 48 + 48 < 12 + 48

n < 60

The sum of two consecutive even integers is 118. Find the smaller of the two integers.

Answers

Answer:

58 + 60

Step-by-step explanation:

Even integers are always seperated by 2.

Which expression is equivalent to 9m – 36?

A. 9(m – 36)
B. 8m – 12 + m + 48
C. 9(m + 4)
D. -12m + 4 + 21m – 40

Answers

The expression is equivalent to 9m-36 is
D is the right answer

You roll a 6-sided number cube with faces numbered 1-6. What is (P)5?

Answers

Answer:

1/6

Step-by-step explanation:

I think it’s 1/6
I hope it’s help

Find the value ot x to the nearest tenth. х 3 9 3​

Answers

x = √63
good luck :)))

Suzanne is baking cupcakes. Her cupcake recipe calls for 314 cups of flour. Suzanne has already added 235 cups of flour. How much more flour does Suzanne need to add in order to reach the amount called for in the recipe? Enter your answer as a fraction.

Answers

Answer:

179

Step-by-step explanation: First you would wanna add 70, to get to 100.

Then, add 9 to get to 314. add 70+9, that is your final answer.

TTQA: Suzanne needs to add 79 more cups of flour, to get to the anount called for in the recipe.

When a number is increased by 23. the result is 42. What equation fits this statement?​

Answers

Answer:

n + 23 = 42

Step-by-step explanation:

Well, let's see.

Let's name the number "n".

So, n + 23 = 42.

And there's your answer.

Hope this helped! :)

Answer:

y + 23 = 42

y = 19

Step-by-step explanation:

y + 23 = 42

Subtract 23 from both sides:

y + 23 - 23 = 42 - 23

y = 19

You have a moving box with a volume of 16 ft3. You know that the box has a length of 2 ft and a height of 4 ft, but you don’t know the width. You need to know all three dimensions to make sure it can fit in the back of the truck. What is the width of the box?
3 ft
4 ft
2 ft
5 ft

Answers

Answer:

2ft

Step-by-step explanation:

The width of the box is 2 ft.

Here,

Volume of box = 16 ft^3

Length of box = 2 ft

Height of box = 4 ft

We have to find the width of box.

What is Volume of box?

The volume of box is defined as, the multiply of length, width, height.

Now,

Volume of box = 16 ft^3

Length of box = 2 ft

Height of box = 4 ft

Since, Volume of box = Length x width x height

Let width of box is x ft.

Volume of box = 2 * x * 4

16 = 8x

x = 2

Hence, The width of the box is 2 ft.

Learn more about the volume visit:

https://brainly.com/question/15102472

#SPJ2

While unwrapping his birthday present, Marcos was very careful to not tear any gift-wrap. When he was done, he laid the gift-wrapping paper flat like shown. Assuming there was no overlapping paper, what was the Total Surface Area of the box his present was in?

Answers

9 x 9 is 81 x 15 is 81 x 5 is 405. 10 x 81 is 810

Pls pls help !!! I rlly need it pls

Answers

Answer:

The x-intercepts of this quadratic function would be (-1, 0) and (4, 0).

Step-by-step explanation:

The x-intercepts of a function are where the graph of the function hits the x-axis on a coordinate plane, meaning the y-coordinate of an x-intercept would always be 0. In this quadratic function's graph, the parabola crosses the x-intercept at two points: (-1, 0) and (4, 0). So that would be the correct answer.

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