differentiate the given function:​

Differentiate The Given Function:

Answers

Answer 1

Answer:

[tex]\displaystyle h'(x) = \frac{1 + x - arcsin(x)\sqrt{1 - x^2}}{\sqrt{1 - x^2}(1 + x)^2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Algebra II

Simplifying

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Special Trig Derivatives:

Arcsine:                                                                                                         [tex]\displaystyle \frac{d}{dx}[arcsin(x)] = \frac{1}{\sqrt{1 - x^2}}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle h(x) = \frac{arcsin(x)}{1 + x}[/tex]

Step 2: Differentiate

Quotient Rule:                                                                                               [tex]\displaystyle h'(x) = \frac{(1 + x)\frac{d}{dx}[arcsin(x)] - \frac{d}{dx}[1 + x][arcsin(x)]}{(1 + x)^2}[/tex]Special Trig Derivative [Arcsine]:                                                                 [tex]\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - \frac{d}{dx}[1 + x][arcsin(x)]}{(1 + x)^2}[/tex]Derivative Property [Addition/Subtraction]:                                                 [tex]\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - (\frac{d}{dx}[1] + \frac{d}{dx}[x])[arcsin(x)]}{(1 + x)^2}[/tex]Basic Power Rule:                                                                                         [tex]\displaystyle h'(x) = \frac{(1 + x)(\frac{1}{\sqrt{1 - x^2}}) - 1[arcsin(x)]}{(1 + x)^2}[/tex]Multiply:                                                                                                         [tex]\displaystyle h'(x) = \frac{\frac{1 + x}{\sqrt{1 - x^2}} - arcsin(x)}{(1 + x)^2}[/tex]Rewrite [Multiply]:                                                                                         [tex]\displaystyle h'(x) = \frac{\frac{1 + x}{\sqrt{1 - x^2}} - arcsin(x)}{(1 + x)^2} \cdot \frac{\sqrt{1 - x^2}}{\sqrt{1 - x^2}}[/tex]Simplify [Multiply]:                                                                                         [tex]\displaystyle h'(x) = \frac{1 + x - arcsin(x)\sqrt{1 - x^2}}{\sqrt{1 - x^2}(1 + x)^2}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e


Related Questions

If f(x) = 8x2 + 4x - 12. Find f(2)
f(2)=

Answers

Answer:

f(2) = 28

Step-by-step explanation:

[tex] \rm f(x) = 8 {x}^{2} + 4x - 12 [/tex]

[tex] \rm Evaluate \: 8 x^2 + 4 x - 12 \: where \: x = 2: \\ \\ \rm \implies f(2) = 8 \times {2}^{2} + 4 \times 2 - 12 \\ \\ \rm \implies f(2) = 8 \times 4 + 8 - 12 \\ \\ \rm \implies f(2) = 32 - 4 \\ \\ \rm \implies f(2) = 28[/tex]

E E E HEY PLEASE HELP. IM LITERALLY ABOUT TO END MYSELF.

Answers

Answer:

( 5 , - 2 )

Step-by-step explanation:

( 10 × [tex]\frac{1}{2}[/tex] , - 4 × [tex]\frac{1}{2}[/tex] ) = (5, - 2)

What value of v makes the equation 3.1v + 1 = 2.5v – 3.5 true

Answers

Answer:

-7.5

Step-by-step explanation:

Answer:

What value of v makes the equation 3.1v + 1 = 2.5v – 3.5 TRUE? Show your work.

Step-by-step explanation:

where n 2 1
OS – On -3
1-
Mn
(
01'0
-
1
)
=
"
n

Answers

I dont understand can u put the question in full form

A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 2 yards long and a plane view (from above) of the shed and field is shown below. Use this information for Parts A and B below.
Part A: Calculate the area of grass that the goat can eat.
Part B: What length of rope would enable the goat to eat 30 square yards of grass? Show all your reasoning.

Answers

Answer:

9.42 yd²3.57 yd

Step-by-step explanation:

Part A

The area of circle with radius of 2 yd (the length of the rope) is:

A = π*r² = 3.14*2² = 12.56 yd²

Since 1/4 of the circle is occupied by the shed, the area of the grass is:

12.56*3/4 = 9.42 yd²

Part B

Let the area be 30 yd², finding the r as per above formula:

3/4*3.14*r² = 30r² = 30*4/3*3.14r² = 12.74r = √12.74r = 3.57 yd

A recipe uses 2 eggs to make 24
cookies. How many cookies could
you make with 9 eggs?

Answers

Answer:

49-50 cookies

Step-by-step explanation:

Hope this was helpful, Have a Wonderful Day!!

What is the formula for finding distance?

Answers

Answer:Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points. Created by Sal Khan and CK-12 Foundation

Step-by-step explanation:

what is the value of y when x = 43

PLS HELPP

Answers

Answer:

Hi there~

y=87

X side. Y side  

1. 3

2. 5

3. 7

4. 9

5. 11

Step-by-step explanation:

We can see that ix x = 1 and y = 3, then that means 1+2

then its 2+3 then 3+4 and so on

So 43 + 44 = 87

So y should equal 87 :)

In a country, 31 % of the people that voted for candidate AA are women. Moreover, 10% of the population are women and voted for A. What is the percentage of people that voted for candidate AA?

Answers

This question is incomplete, the complete question is;

In a country, 31 % of the people that voted for candidate AA are women. Moreover, 10% of the population are women and voted for AA. What is the percentage of people that voted for candidate AA?

Answer:

the percentage of people that voted for candidate AA is 32.3%

Step-by-step explanation:

Given that;

31 % of the people that voted for candidate A are women

P( women/Candidate AA) = 0.31

Moreover, 10% of the population are women and voted for AA

P( women & candidate AA) = 0.10

so

p( Candidate AA) =  P( women & candidate AA) / P( women/Candidate AA)

p( Candidate AA)  = 0.10 / 0.31

p( Candidate AA)  = 0.323

p( Candidate AA)  = 32.3%

Therefore the percentage of people that voted for candidate AA is 32.3%

Please check #9 and tell me if I’m right
Q: Find (x) so the (L) is parallel to (m) and state the converse used

Answers

Answer:

that's 53 °not 90 i thought

PLEASE ANSWER ASAP!!!



A right triangle always has obtuse exterior angles at two verticies, True or False?

Answers

Answer:

false

Step-by-step explanation:

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 451451 watts with a variance of 144144. What is the probability that the mean amplifier output would be greater than 449.8449.8 watts in a sample of 7676 amplifiers if the claim is true?Round your answer to four decimal places.

Answers

Answer:

The probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers is 0.8078.

Step-by-step explanation:

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is as follows:

[tex]\mu=451\\\sigma^{2}=144\\n=76\\\bar x=449.8[/tex]

Compute the probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers as follows:

[tex]P(\bar X>449.8)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{449.8-451}{\sqrt{144/76}})\\\\=P(Z>-0.87)\\\\=P(Z<0.87)\\\\=0.8078[/tex]

*Use a z-table.

Thus, the probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers is 0.8078.

A business is owned by 3 people. Mrs. Applegate owns
3
19
of the business. Mrs. Brown owns 3 times as much as
Mrs. Charles. What fractional part of the business does Mrs. Brown own?

Answers

Given:

Mrs. Applegate owns  [tex]\dfrac{3}{19}[/tex] of the business.

Mrs. Brown owns 3 times as much as  Mrs. Charles.

To find:

The  fractional part of the business that Mrs. Brown owns.

Solution:

Let Mrs. Charles owns x part of business.

Mrs. Brown owns 3 times as much as  Mrs. Charles.

Mrs. Brown owns = 3x part of business.

Mrs. Applegate owns  [tex]=\dfrac{3}{19}[/tex] of the business.

[tex]x+3x+\dfrac{3}{19}=1[/tex]

[tex]4x=1-\dfrac{3}{19}[/tex]

[tex]4x=\dfrac{19-3}{19}[/tex]

[tex]4x=\dfrac{16}{19}[/tex]

Divide both sides by 4.

[tex]x=\dfrac{16}{4\times 19}[/tex]

[tex]x=\dfrac{4}{19}[/tex]

Now,

Mrs. Brown owns  [tex]=3\times x[/tex]

[tex]=3\times \dfrac{4}{19}[/tex]

[tex]=\dfrac{12}{19}[/tex]

Therefore, Mrs. Brown owns  [tex]\dfrac{12}{19}[/tex] of the business.


Order the numbers from least to greatest.

Answers

Answer: -11/2, -5/7, 0.1, 4/5, 1.3

Step-by-step explanation:

It might be easier to convert these fractions into decimals so let’s do that. -5/7 becomes about -0.7, 4/5 becomes 0.8, 1.3 is already a decimal, -11/2 becomes -5.5, and 0.1 is already a decimal. Negative numbers are less than positive numbers and -5.5 is a bigger negative number than -0.7, so -5.5 (-11/2) comes first and -0.7 (-5/7) comes second. 0.1 is less than 0.8 so 0.1 is third and 0.8 (4/5) is fourth. That leaves 1.3 as the greatest number. This gives us the list -11/2, -5/7, 0.1, 4/5, 1.3. Hope this helps!

8 Dvided by 3/5 HELP MEEEEEEEE

Answers

Answer:

40/3

Step-by-step explanation:

The senior class sells movie tickets to students and teachers. The student tickets cost $4 each and teacher tickets cost $8 each. If they earned only $44, how many possible combinations of student and teacher tickets could have been sold?

Answers

5 teachers & 1 student
4 teachers & 3 students
3 teachers & 5 students
2 teachers & 7 students
1 teacher & 9 students

Answer: 5 possibilities

How can a percent be used to describe a change in quantity?

Answers

Answer:

remember,a percent means "per 100".You can describe the change as a fraction comparing the amount of change to the original and then use a proportion to rewrite your problem as a percentage out of 100.

A manufacturer produces bolts of a fabric with a fixed width. The cost of producing x yards of this fabric is C = f(x) dollars.

Required:
a. What is the meaning of the derivative fâ'(x)? What are its units?
b. In practical terms, what does it mean to say that fâ'(2,000) = 10?
c. Which do you think is greater, fâ'(200) or fâ'(600)? What about fâ'(4,000)?

Answers

Correct is;

A manufacturer produces bolts of a fabric with a fixed width. The cost of producing x yards of this fabric is C = f(x) dollars.

(a) What is the meaning of the derivative f '(x)?

What are its units?

(b) In practical terms, what does it mean to say that f '(2000) = 10?

(c) Which do you think is greater,

f '(200) or f '(600)? What about f '(4000)?

Answer:

A) f'(x) means the rate of change of the cost of production with respect to the number of yards that were produced.

It's unit is $/yard

B) f '(2000) = 10 means that after production of 2000 yards of fabrics, the cost of production will be increasing at a rate of $10 per yard.

C) f' (200) > f'(600)

f'(4000) > f'(600)

Step-by-step explanation:

A) Since the cost of producing x yards of this fabric is C = f(x) dollars. f'(x) simply means the rate of change of C with respect to x.

In clearer terms, the derivative f'(x) means the rate of change of the cost of production with respect to the number of yards that were produced.

It's unit is $/yard

B) To say f '(2000) = 10 means that after production of 2000 yards of fabrics, the cost of production will be increasing at a rate of $10 per yard.

C) f '(200) is greater than f'(600) because the cost of making the 600th yard will be less than the cost of the 200th yard. Reason for this is due to economics of scale as the manufacturer will certainly make more efficient use of fixed costs of production.

As more units are produced, there may likely be more overtime costs and thus the rate of increase cost of production will likely increase faster.

Thus;

f'(4000) > f'(600)

Misty wants to save money to purchase a new bicycle that costs $279. She
opens a savings account and deposits $7 per week. How many weeks will it
take for her to save enough money to buy the bicycle?

Answers

Answer: Hmm, I want to say it will be about 40 weeks before she can get the bike, hope this helps!

Step-by-step explanation:

Answer:

40 weeks

Step-by-step explanation:

Let's pretend you are interested in learning what music teens prefer.
Choose a survey setup below that would most likely represent teens the
best. Add a post to the discussion board that identifies which option you
think is the best representation and why. Also, take a moment to read
the observations posted by your peers. Choose two different posts to
respond to and explain why you agree or disagree with your classmate.
Option 1: You stand outside of the grocery store and ask 100 people
what type of music they prefer.
Option 2: You randomly draw 100 names from a hat of students at your
school, and ask those students what type of music they prefer.
Option 3: You randomly select 2 neighborhoods in your town and ask 50
people in each neighborhood what type of music they prefer.

Answers

Answer:

option 2

Step-by-step explanation:

when dividing 592 by 9.25, how many zeros will be placed in the dividend?

A: one

B: two

C: three

D: four​

Answers

Answer: two

While you are dividing by a decimal you play a zero until it is the same place a the dividend

IF UR GOOD AT PRECALC PLEASE HELP

Answers

Answer:

Answer is C, u can find this just by looking at domain

The answer is C hope this helps

Solve for: 22≥4m-2 or 5-3m≤-13

Answers

Answer:

22≥4m-2=6

5-3m<-13=6

Step-by-step explanation:

The inequalities  22 ≥ 4m - 2 or 5 - 3m ≤ - 13 is m ≤ 6 or m ≥ 6.

What are inequalities and their types?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

22 ≥ 4m - 2.

4m ≤ 22 + 2.

4m ≤ 24.

m ≤ 24/4.

m ≤ 6.

5 - 3m ≤ - 13.

- 3m ≤ - 13 - 5.

- 3m ≤ - 18.

3m ≥ 18.

m ≥ 18/3.

m ≥ 6.

So, m ≤ 6 or m ≥ 6.

learn more about inequalities here :

https://brainly.com/question/30228778

#SPJ2

Determine the value of x if y=3
y = 2x+3

Answers

Answer:

0

Step-by-step explanation:

3 = 2x + 3

0 = 2x

x = 0

How many cups are in 3 gallons? 1 gallon = 16 cups
Label your answer in cups.

Answers

Answer:

There are 48 cups in 3 gallons!

Hope this helped! :)

3 times what is 5
(whole number if possible)

Answers

Answer:

1.6, but can be rounded to 2

Step-by-step explanation:

Answer:

1.66

Cannot be a whole number because 3 times a whole number cannot equal 5

Select the correct answer.


What is the relationship between the two shapes?

LOOK AT THE IMAGE PLEASE

Answers

The answer is the A because they are similar and congruent

Answer:

A

Step-by-step explanation:

Which of the following represents the prime factortzation of 72?
023.32.4
th
023.32
02.32.42
22.33

Answers

Answer:

2³ x 3²

Step-by-step explanation:

The prime factorization of a number is the process of breaking down a number to a set of prime numbers that their product will give the original number:

          72

      2   x    36

      2 x 2 x 18

      2 x 2 x 2 x 9

       2 x 2  x 2 x 3 x 3

So;

  The prime factorization is 2³ x 3²

Find the value of X, I need help solving this

Answers

It’s 13
13times 4 is 52

Answer:

B) 13

Step-by-step explanation:

The given angles are vertical angles and has same measurement

4x = 52° divide both sides by 4

x = 13

A baseball is thrown in a parabolic arch

Answers

cool stuff !!!!!!!! lol is that all
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