Answers
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 RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationAlgebra II
SimplifyingCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative 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
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
A baseball is thrown in a parabolic arch
Answers
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
8 Dvided by 3/5 HELP MEEEEEEEE
Answers
Answer:
40/3
Step-by-step explanation:
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%
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:
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:
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:
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
IF UR GOOD AT PRECALC PLEASE HELP
Answers
Answer:
Answer is C, u can find this just by looking at domain
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.
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! :)
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
4 teachers & 3 students
3 teachers & 5 students
2 teachers & 7 students
1 teacher & 9 students
Answer: 5 possibilities
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 :)
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 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:
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 ydStep-by-step explanation:
Part AThe area of circle with radius of 2 yd (the length of the rope) is:
A = π*r² = 3.14*2² = 12.56 yd²Since 1/4 of the circle is occupied by the shed, the area of the grass is:
12.56*3/4 = 9.42 yd²Part BLet 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 ydwhen dividing 592 by 9.25, how many zeros will be placed in the dividend?
A: one
B: two
C: three
D: four
Answers
While you are dividing by a decimal you play a zero until it is the same place a the dividend
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)
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
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.
PLEASE ANSWER ASAP!!!
A right triangle always has obtuse exterior angles at two verticies, True or False?
Answers
Answer:
false
Step-by-step explanation:
Find the value of X, I need help solving this
Answers
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
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
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.
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:
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)
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]
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!
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