Answers
Answer:
h'(x)= [tex]e^{x^{9}+In(x) } (9x^{8} +\frac{1}{x} )[/tex]
Step-by-step explanation:
h(x)=[tex]e^{x^{9} +In(x)}[/tex]
first, we will use the chain rule
step1: we divide the function into two parts So,
f(x)=[tex]e^{x^{9} +In(x)}[/tex] and g(x)=[tex]x^{9} +In(x)[/tex]
step2: rewrite [tex]x^{9} +In(x)[/tex] as u.
f(x)=[tex]e^{u}[/tex] and g(x)=u
step3: differentiate f(x) first.
f'(x)=[tex]e^{u}[/tex] (the formula is y=[tex]e^{x}[/tex] and y'=[tex]e^{x}[/tex] - the same)
step4: write the value of u for each function but now sub it in the differentiable form of f(x).
f'(x)=[tex]e^{x^{9}+In(x) }[/tex] and g(x)=[tex]x^{9}+In(x)[/tex]
step5: differentiate the function g(x).
g'(x)=[tex]9x^{8} +\frac{1}{x}[/tex]
(for [tex]x^{9}[/tex] the formula is y=[tex]x^{n}[/tex] and y'=[tex]nx^{n-1}[/tex] ) (for In(x) the formula is y=In(x) and y'=[tex]\frac{1}{x}[/tex] )
step6: use the chain rule to finish out So,
h'(x)=f'(x) × g'(x)
=[tex]e^{x^{9}+In(x) }[/tex] × [tex]9x^{8}+\frac{1}{x}[/tex]
step7: simplify.
h'(x)= [tex]e^{x^{9} +In(x)}(9x^{8}+\frac{1}{x})[/tex]
Related Questions
if 2^6=y^3 what is y?
Answers
Answer:
y=4
Step-by-step explanation:
simplify 2^6 --> 64
find the cube root of 64,
y=4
A certain brand of coffee comes in two sizes. A 10.5-ounce package costs $2.99. A 29.3-ounce package costs $7.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Answers
Answer:
The unit price are:
$0.285 for the 10.5 ounce package
$0.272 for the 29.3 ounce package.
The size that is the better buy based on the unit price is the 29.3-ounce package costs $7.98 because it's unit's price($0.272) is lesser than that of the 10.5 ounce package.
Step-by-step explanation:
From the question:
A 10.5-ounce package costs $2.99.
The unit price = 1 ounce.
10.5 ounce = $2.99
1 ounce = x
10.5 ounce × x = 1 ounce × $2.99
x = 1 ounce × $2.99/10.5 ounce
x = $0.2847619048
The unit price = $0.2847619048
Approximately = $0.285
A 29.3-ounce package costs $7.98.
The unit price = 1 ounce.
29.3 ounce = $7.98
1 ounce = x
29.3 ounce × x = 1 ounce × $7.98
x = 1 ounce × $7.98/29.3 ounce
x = $0.2723549488
The unit price = $0.2723549488
Approximately = $0.272
The size that is the better buy based on the unit price is the 29.3-ounce package costs $7.98 because it's unit's price($0.272) is lesser than that of the 10.5 ounce package.
Answer: i did this test
Step-by-step explanation:
PLEASE HELP!
Solve x2 + 5x = −6.
x = 5 and x = 1
x = −5 and x = −1
x = 3 and x = 2
x = −3 and x = −2
Answers
X^2 + 5x = -6
Add 6 to both sides:
X^2 + 5x + 6 = 0
Using the quadratic equation x = -b +/-sqrt(b^2 -4ac )/2a replace the letters with their values and solve for x.
A = 1, b = 5 , c = 6
Solving for x you get -2 and -3
The answer would be x = -3 and x = -2
What is 25 percent of 530?
Answers
:)))))))
3/2x + 8= -1 solve equation
Answers
Answer:
x = -6
Step-by-step explanation:
Subtract 8 from each side, so it now looks like this: 3/2x = -9Divide each side by 3/2 to cancel out the 3/2 next to x. It should now look like this: x = -6I hope this helps!
Answer:
x= -6
Step-by-step explanation:
3/2x+8-8=-1-8
3/2 x= -9
2. 3/2x=2(-9)
3x= -18
3x/3 = -18/3
x= -6
Select ALL the statements that are true about 22/7.
A.It is a rational number.
B.It is an irrational number.
C.When written as a decimal, it repeats.
D.It is an approximate value of Pi.
E.It is a terminating decimal.
Answers
Answer:
It is an approximate value of pi
An artist sells paintings for $100 each. For each painting, the cost of the canvas
is $10 and the cost of the paints is $8.
How much profit (a positive amount of money earned after paying for
the costs) would the artist earn if she were to sell 10 paintings?
Answers
Answer:
820 in profit
Step-by-step explanation:
The artist makes $82 in profit on each painting. 82 x 10 is 820
Marge's plan costs .14 cents per minute plus a monthly fee of $24. Dan's plan costs .12 cents per minute plus a monthly fee of $28. How many minutes (m) are required for both plans to cost the same for the month?
Answers
Answer:
6 min for Marge's and 7 for Dan's plan
Step-by-step explanation:
0.14x6=0.84
0.12x7=0.84
ax+bx=c solve for x
Answers
Answer:
x= c/a+b
Step-by-step explanation:
A car rental company charges a daily rate of $ 27 plus $ 0.1 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $ 45.5. How many miles did you drive? Give your answer to the nearest whole mile. miles
Answers
Answer:
185 miles.
Step-by-step explanation:
According to the given situation, the calculation of mile is shown below:-
Assume drive = x miles
Total bill incurred = ($27 + 0.1 x) = $45.5
Now we will solve the above equation:
0.10x = $45.5 - $27
0.10x= 18.5
x = 18.5 ÷ 0.10
x = 185 miles.
So, the correct answer is 185 miles.
The same is to be considered
Chris ate a total of 100 peanuts in 4 days, each day eating 8 more peanuts than the day before. How many peanuts did he eat on the first day
Answers
Answer:
He ate 68 peanuts on his first day
Step-by-step explanation:
To find the answer, you can just multiply 4 times 8 which would give the total amounts of peanuts Chris ate in 4 days. And subtract 100-32 which would equal 68.
4x - 1 = 2(2x + 2)
what is the answer?
Answers
Answer:
x = undefined
Step-by-step explanation:
Expand brackets
4x - 1 = 4x + 4
Rearrange and make like terms next to each other
4x - 4x = 4 + 1
0x = 5
x = 5/0
when 0 is the denominator the answer is undefined
Answer: from what i calculated there is no solution
Step-by-step explanation:
4. During a 12- hour period, the temperature dropped 48°. How many degrees did the temperature drop each hour.
Is the answer negative or positive? Please help..
Answers
Answer:
-4
Step-by-step explanation:
Can someone tell me them least to greatest please!!!!!
Answers
Answer:
11/3 , 17 , 20 hope this helps
A town has accumulated 4 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated 10 inches, and the depth is increasing by 3 inches every hour. In about how many hours will the snowfall of the towns be equal?
Answers
9514 1404 393
Answer:
2 hours
Step-by-step explanation:
The initial difference in depth is 10-4 = 6 inches. The difference in snowfall rates is 6-3 = 3 inches per hour.
At that rate, the difference in depth will be made up in ...
(6 in)/(3 in/h) = 2 h
In 2 hours the snowfall in the two towns will be equal.
_____
You could write equations for depth, then equate them.
d1 = 4 +6h
d2 = 10 +3h
d1 = d2 . . . . . . . . . . for some value of h the depths will be equal
4 +6h = 10 +3h
h(6 -3) = 10 -4 . . . . . subtract 3h+4 from both sides
h = 6/3 = 2
Snowfall will be equal in 2 hours.
given the function f(x)=(x-2)(x+3)(2x+3), which set includes all of the zeros for the polynomial?
Answers
Answer:
{2, -3, -3/2}
Step-by-step explanation:
hi! we can set each of the binomials equal to 0 to find the zeros of this polynomial.
x-2=0
x=2
x+3=0
x=-3
2x+3=0
2x=-3
x=-3/2
The set includes all of the zeros for the polynomial would be; {2, -3, -3/2}.
What is a polynomial?They are mathematical expressions involving variables raised with nonnegative integers and coefficients(constants that are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.
We have been given the function f(x)=(x-2)(x+3)(2x+3)
Each of the binomials is equal to 0 to determine the zeros of this polynomial.
1. x-2=0
x=2
2. x+3=0
x=-3
3. 2x+3=0
2x=-3
x=-3/2
Hence, the set includes all of the zeros for the polynomial would be; {2, -3, -3/2}.
Learn more about polynomials here:
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please answer i need help
Answers
Answer:
h < 2
Step-by-step explanation:
Given
5(2h + 8) < 60 ( divide both sides by 5 )
2h + 8 < 12 ( subtract 8 from both sides )
2h < 4 ( divide both sides by 2 )
h < 2
Answer:
h<2
Step-by-step explanation:
5(2h+8)<60
2h+8<12
2h<4
h<2
What is 65% of 186. Round to the nearest tenth if necessary
Answers
Answer:
120.9
Step-by-step explanation:
Pls give Brainliest!
Which choice best represents the sum of (5 + 8x - 3) and (9x - 6)
17x +-4
17x + 4
x + 14
x+ - 14
Answers
Answer:
17x−4
Step-by-step explanation:
Let's simplify step-by-step.
5+8x−3+9x−6
=5+8x+−3+9x+−6
Combine Like Terms:
=5+8x+−3+9x+−6
=(8x+9x)+(5+−3+−6)
=17x+−4
At New years you decide to join a gym to lose all those calories gained during winter break and youre comparing two different gyms. The first gym, gym A has a 12$ initiation fee and then costs 10$ per month. The second gym , gym B has a 20$ initiation fee and then costs 6$ per month. Create an equation that aims to find when these two gyms will cost the same amount of money
Answers
Given:
For gym A, initiation fee = $12 and cost = $10 per month.
For gym B, initiation fee = $20 and cost = $6 per month.
To find:
The equation that aims to find when these two gyms will cost the same amount of money,
Solution:
Let the number of months be x.
Cost function = Initiation fee + (cost)(x)
Cost function for gym A is
[tex]f(x)=12+10x[/tex]
Cost function for gym B is
[tex]g(x)=20+6x[/tex]
Cost of these two gyms are equal if f(x)=g(x).
[tex]12+10x=20+6x[/tex]
Therefore, the required equation is [tex]12+10x=20+6x[/tex].
On solving this equation, we get
[tex]10x-6x=20-12[/tex]
[tex]4x=8[/tex]
[tex]x=2[/tex]
Hence, after 2 months the cost of these two gyms are same.
Why is the base of the parallelogram 1/2 the circumference of the circle?
Answers
Consistent System of Equations
In other words.:Counterclockwise of negative x positive + the absolute value of 18 - 45 will equal 1/2
A runner sprinted for 117 yards (yd). How many feet (ft) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation. ft mi yd 1760 yd 1 mi 3 ft 1 ft 12 in 1 yd Ratios: 1 mi 1760 yd 1 yd 3 ft 12 in 1 ft . in Х 117 yd 1 ft 0 x IK IT LOOKS CONFUSING SO LOOK AT THE PICTURE HELP ME PLEASE!!!!:)
Answers
Answer:
117 yd/1 x 3 ft/1 yd = 351 ft
Step-by-step explanation:
[tex]\frac{117}{1} * \frac{3}{1} = 351 ft[/tex]
A runner sprinted for 351 feet.
Given that, a runner sprinted for 117 yards (yd).
How to convert yards to feet?To convert a yard measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the yards multiplied by 3.
Here, multiply the ratio 117/1 by 3/1.
That is, 117 × 3 =351 ft
Therefore, a runner sprinted for 351 feet.
To learn more about the metric conversion visit:
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Cassie has a rectangular window that is 40 Inches long and 25 inches wide. She wants to put a metal frame around the edges of her window. How many inches of metal frame will she need? Please help me
Answers
Answer:
she will need 130 inches lf metal
Step-by-step explanation:
One side lf the window is 40 and the other side lf the window is 25 ,so just multiply those by 2.That will give you 50 and 80 just add those together and you get 130
PLSSS HELPPP ASAPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!
An underground mine elevator descends 12% of the total depth every minute. The total depth of the elevator is 75 meters below the ground. How many meters below the ground is the elevator after 2 minutes?
1. −18 meters
2. −9 meters
3. −4.5 meters
4. −22.5 meters
Answers
Answer:
I believe its 1. -18 meters
Step-by-step explanation:
first find how many meters the elevator is descending per minute. to do this:
what is 12% of 75?
(75×.12) = 9
the elevator is descending 9 meters per minute.
9×2=18
10x+y when x = 7 and y = 5
Answers
Answer: 75
Step-by-step explanation:
Plug in 7 for x and 5 for y
10(7)+5
70+5
75
Circle A has a diameter of 9 , Circle B has a radius of 5 , how many centimeters larger is it ?
Answers
Answer:
4
Step-by-step explanation:
A country is dealing with a serious macroeconomic problem. Businesses
around the country have been shutting down, leaving millions of people out of
work. Even citizens with a high level of education and technical skills are
struggling to find jobs.
Which problem is this country dealing with?
A. A high unemployment rate
B. A high level of inflation
C. A low per capita GDP
D. A rapid growth in GDP
Answers
Answer:
A: A high unemployment rate
Step-by-step explanation:
A high unemployment rate is the problem which is dealing by the country
What is Business?Business is the practice of making one's living or making money by producing or buying and selling products.
Given that a country is dealing with a serious macroeconomic problem. Businesses around the country have been shutting down, leaving millions of people out of work.
Even citizens with a high level of education and technical skills are
struggling to find jobs.
This problem is dealing with high unemployment rate.
Unemployment is a measure of the percentage of the labor force that is without work but actively seeking employment.
By given data it suggests that many businesses have shut down, leading to a significant increase in the number of people who are out of work. This situation is often referred to as a high unemployment rate.
Hence, a high unemployment rate is the problem which is dealing by the country.
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2 + 29m - 9m - 5 =
HELP
Answers
Answer:
20m-3
Step-by-step explanation: hope that helps :)
2+29m−9m−5
=2+29m+−9m+−5
Combine Like Terms:
=2+29m+−9m+−5
=(29m+−9m)+(2+−5)
=20m+−3
The distribution of annual profit at a chain of stores was approximately normal with mean \mu = \$66{,}000μ=$66,000mu, equals, dollar sign, 66, comma, 000 and standard deviation \sigma = \$21{,}000σ=$21,000sigma, equals, dollar sign, 21, comma, 000. The executives conducted an audit of the stores with the lowest 20\%20%20, percent of profits. What is closest to the maximum annual profit at a store where the executives conducted an audit?
Answers
Answer:
The closest to the maximum profit is [tex]x = \$ 83682[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$66,000[/tex]
The standard deviation is [tex]\sigma = \$ 21000[/tex]
The percentage of profit is 20%
Generally the closest to the maximum annual profit at a store where the executives conducted an audit is mathematically evaluated as follows
[tex]P(X > x ) = 0.20[/tex]
=> [tex]P(X > x ) = P(\frac{X -x}{\sigma } > \frac{x -66000}{21000} ) = 0.20[/tex]
From the z-table the z-score for 0.20 is
[tex]z-score = 0.842[/tex]
So
[tex]\frac{x -66000}{21000} = 0.842[/tex]
=> [tex]x = \$ 83682[/tex]
Answer:
48,000
Step-by-step explanation:
Write 3.01 repeating as a mixed number.
Answers
Answer:
3 1/100
Step-by-step explanation:
Place the decimal number over a power of ten.