Let f(x)=5x^4 and g(x)=e^2x+x. If h is the function defined by h(x)=f(g(x)), which of the following gives a correct expression for h′(x)?
Answers
The values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 ).
Option C is the correct answer.
Given,
f(x)=5x^4 and g(x)=e^2x+x.
If h is the function defined by h(x)=f(g(x)),
We need to find h′(x).
What is the differentiation formula for the following?We have,
dx/dx = 1
d[tex]x^{n}[/tex]/dx = n[tex]x^{n-1}[/tex]
d[tex]e^{x}[/tex]/dx = [tex]e^{x}[/tex]
d[tex]e^{n}[/tex]/dx = [tex]ne^{n}[/tex]
d(cx)/dx = c(dx/dx) = c
We have,
- f(x)=5[tex]x^{4}[/tex] ______(1)
- g(x)=[tex]e^{2x}[/tex]+x ______(2)
- h(x)=f(g(x)) _______(3)
Now,
h(x) = f ( [tex]e^{2x}[/tex]+x )
From (1)
h(x) = 5[tex](e^{2x} + x) ^{4}[/tex] ______(4)
Now,
Differentiate (4)
h'(x) = 5 d[tex](e^{2x} + x) ^{4}[/tex]/dx
h'(x) = 5 x 4 [tex](e^{2x} + x) ^{3}[/tex] d [tex](e^{2x} + x)[/tex] / dx
h'(x) =20 [tex](e^{2x} + x) ^{3}[/tex] ( d[tex]e^{2x}[/tex]/dx + dx/dx )
h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 )
Thus the values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 ).
Option C is the correct answer.
Learn more about differentiation here:
https://brainly.com/question/24062595
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Related Questions
what are the different types of polygons need it for my primary school sis
Answers
Answer:
Regular Polygons.
Irregular Polygons.
Concave Polygons.
Convex Polygons.
Trigons.
Quadrilateral Polygons.
Pentagon Polygons.
Hexagon Polygons.
Which number is irrational?
Ο Α. π
Ο Β. 0.333...
Ο C. 0.7
Ο D. 0.277277277...
Answers
Answer:
A.π is the correct answer
2. What is the value of the pass after 15 rides?
# of Rides Bus Pass Value Rule
0 $100.00
1 $98.25
2 $96.50
3 $96.75
15 ??? $73.75 ??? Is my answer 73.75 right? If not does anyone know the correct answer
!plz help!
Answers
Answer:
im really confused. but its 2,75$ per pass?/ride? sorry i cant help much
Step-by-step explanation:
Given that ∠A≅∠B, Evelia conjectured that ∠A and ∠B are acute angles.
Which statement is a counterexample to Evelia's conjecture?
1. m∠A=126° and m∠B=126°
2. m∠A=114° and m∠B=170°
3. m∠A=30° and m∠B=40°
4. m∠A=45° and m∠B=45°
Answers
Answer:
answer is choice 4 because in te given angle A and angle B are congrunt and if they are acute the degree measure is 0-90
Akeem bought a used video game for $38. Later, he sold it for 40% less than he paid. For how much did he sold the video game? please help, WITH EXPLANATION ASWELL !!
Answers
Answer:
£22.8
Step-by-step explanation:
Akeem bought a used video game for $38. Later, he sold it for 40% less than he paid.
First, find
40% of £38
=£15.2
Then, find the price of which he sold the video game for...
£38 – £15.2
= £22.8
Hope this helped you- have a good day bro cya)
Graph f(x) = -2/3x - 3
Answers
Answer:
go to desmos. com there's a free graphing calculator that helps
If f(x) = 5x + 4 what is the value of f(-2) ?
Answers
5(-2) + 4 = ? (Multiply -2)
-10 + 4 = -6
Answer:
-6
Step-by-step explanation:
Take the x out for -2
f(-2) is equivalent to x=-2
f(x) = 5x + 4
1. f(-2)=5(-2)+4
2. f(-2)= -10+4
3. -6
(14.7+9.3) times (1/2)2
Answers
Answer:
24
Step-by-step explanation:
A customer buys
3
shirts that cost
$
10
each. The store is having a sale for
15
%
off, and the sales tax is
6
%
. The store applies discounts before applying the sales tax to a customer’s total.
What is the customer’s total after the discount and sales tax are applied, in dollars and cents?
Answers
Answer:
4.77
Step-by-step explanation:
3 x 10 = 30
30 % 15 = 4.5
4.5 % 6 = 0.27
0.27 + 4.5 = 4.77
can someone please explain this
Answers
Answer:
11) is a
12) all answers are incorrect just put b
Step-by-step explanation:
Answer:
あなたをあきらめるつもりはありません
リック・アストリーの歌
Step-by-step explanation:私たちは愛する見知らぬ人ではありません
あなたはルールを知っています、そして私もそうです
完全なコミットメントは私が考えていることです
あなたは他の人からこれを取得しないでしょう
気分を伝えたいだけです
お奨めはあなたに理解させる
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
私たちは長い間お互いを知っていました
あなたの心は痛んでいますが、あなたはそれを言うには恥ずかしがり屋です
内部では、私たち二人は何が起こっているのかを知っています
私たちはゲームを知っていて、それをプレイするつもりです
そして、あなたが私にどのように感じているか尋ねれば
あなたが盲目すぎて見ることができないと私に言わないでください
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
決して与えるつもりはない、決して与えるつもりはない
（あきらめて）
私たちは長い間お互いを知っていました
あなたの心は痛んでいますが、あなたはそれを言うには恥ずかしがり屋です
内部では、私たち二人は何が起こっているのかを知っています
私たちはゲームを知っていて、それをプレイするつもりです
気分を伝えたいだけです
お奨めはあなたに理解させる
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
嘘をついてあなたを傷つけることは決してない
あなたをあきらめるつもりはありません
決してあなたを失望させるつもりはありません
走り回ってあなたを捨てるつもりはない
泣かせないで
さよならを言うつもりはない
Each cube in the prism is one cubic unit.
What is the volume of this rectangular prism
Answers
Answer:
I don't have answer but To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units
Answer:
The volume of this rectangular prism is 90.
Step-by-step explanation:
V = L * W * H
V = 6 * 3 * 5
GHD989 guys please you this code for guathmath thank you .
Answers
I will do that soon okay I will
if x = (7+4√3), then the value of x^2 + 1/x^2 is
Answers
Answer:
194.
Step-by-step explanation:
x = (7+4√3)
x^2 = x = (7+4√3)^2
= 49 + 48 + 56√3
= 97 + 56√3
x^2 + 1/x^2 = 97 + 56√3 + 1/(97 + 56√3)
= 194.
By which rule are these triangles congruent. A. AAS B. ASA C. SAS D. SSS
Answers
the function is( -7,1)(-5,3)(-7,-1)(5,13)
Answers
Answer:
Not a function
Step-by-step explanation:
The an x-value (the first number in your ordered pair)ca not appear in another ordered pair. It it does, you do not have a function.
( -7,1)(-5,3)(-7,-1)(5,13) -7 appears as the first number in two of your ordered pairs. Not a function!
Juna travels 15 mph for 10 hours find the distance piles per hour
Answers
Answer:2 hours 15 mins = 2 1/4 hours
2 1/4 hours = 25 miles
1 hour = 25 ÷ 2 1/4 = 25 ÷ 9/4 = 25 x 4/9 = 11.1 miles
Answer: 11.1 mph
Step-by-step explanation:
-
What is the equation of the line that passes through the point (-4,-7) and has a
slope of?
Answers
Answer:
y = -4 x -9
Step-by-step explanation:
If it wrong i'm sorry
The quality assurance department at a gear found that there were 3 defective gears for every 500 produced. Write this as a fraction and as a precent. Please explain
Answers
Answer:
3/500
Step-by-step explanation:
Which graph represents the polynomial function f(x)=x3+4x2−1
Answers
Answer:
B OK HOI THE FIRST TIME I AM SO SORRY TO
A jewelry supply shop buys silver chains from a manufacturer for c dollars each, and then sells the chains at a 57-percent markup. Write the markup as a decimal, A expression for the retail price silver chain, a retail price of a silver chain purchased for 45 dollars, and how much was added to the original price of the chain
( if you answer all the questions i will mark you the Brainy-est. )
Answers
The amount added to the original price of the jewelery is the Markup price. Hence, the amount added is $16.34
Markup = 57% = 0.57Cost of jewellery = cRetail price = $45Retail price = cost of jewellery + Markup
$45 = c + 0.57c
45 = 1.57c
Divide both sides by 1.57
c = 45/1.57
c = $28.66
The Markup price = (Retail price - Original price)
Markup = $45 - $28.66 = $16.34Therefore, the amount added to the original price is $16.34
Learn more : https://brainly.com/question/18796573
please help me i’m being timed
Answers
B) No because an equilateral triangle has 3, 60 degree angles so it cannot be a right-angle triangle.
The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let’s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 656 exams in his state. The sample mean for the test is 480.
Find the 95% confidence interval to estimate the mean SAT math score in this state for this year.
(Note: The critical
z
-value to use,
z
c
, is: 1.960.)
( , )
Answers
Using the z-distribution, it is found that the 95% confidence interval to estimate the mean SAT math score in this state for this year is (472, 488).
We have the standard deviation for the population, which is why the z-distribution is used to solve this question.
The sample mean is [tex]\overline{x} = 480[/tex].The population standard deviation is [tex]\sigma = 100[/tex].The sample size is [tex]n = 656[/tex].The interval is given by:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.
Then:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 480 - 1.96\frac{100}{\sqrt{656}} = 472[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 480 + 1.96\frac{100}{\sqrt{656}} = 488[/tex]
The 95% confidence interval to estimate the mean SAT math score in this state for this year is (472, 488).
A similar problem is given at https://brainly.com/question/22596713
8 7/3 divided 7 1/2
6 1/2 divided 34/4
23/3 divided 6 2/5
Pls help ASAP
Answers
1) 1 17/45
First:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
31/3 ÷ 15/2
Applying the fractions formula for division,
= 31 × 2/3 × 15
= 62/45
Simplifying 62/45, the answer is
1 17/45
2) 13/17
First:
Convert any mixed numbers to fractions.
Reduce fractions where possible.
Then your initial equation becomes:
13/2 ÷ 17/2
Applying the fractions formula for division,
= 13 × 2/2 × 17
= 26/34
Simplifying 26/34, the answer is
13/17
3) 1 19/96
First:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
23/3 ÷ 32/5
Applying the fractions formula for division,
= 23 × 5/ 3 × 32
=115/96
Simplifying 115/96, the answer is
1 19/96
A college student takes out a $7 500 loan from a bank. Assuming the student has not started paying back the money, how much does the student owe . . .
1.1 . . . after 1 year, if the bank charges 3.8% interest each year?
Answers
So the time period in the compounding equation is YEARS.
The compounding equation is:
(Future Loan Amount) = (Current Loan Amount) * (1 + the interest rate of the time period in decimals) ^ (number of time periods)
(Use this for all future questions too - if compounding monthly then time period is total number of months and interest rate is annual rate divided by 12 etc)
So in this case the answer is:
(Future Loan Amount) = (Current Loan Amount) * (1 + the interest rate of the time period in decimals) ^ (number of time periods)
(Future Loan Amount) = $7,500 * (1 + 0.038) ^ (11) = $11,304
(note - when answering its hard to see the original question. I believe the answer asked for 11 years. If not, if 1 year, etc just plug in that number into the equation - so one year is simply: 7500*1.038 = $7,785
helpppppppp plzzzzzzzzzzzzzzzzz (ANSWER ONLY IF YOU KNOW)
Answers
Answer:
1/7 ( a+1 )
Step-by-step explanation:
1/7a + 1/7
1/7 ( a+1 )
Out of the four benefits of direct deposit (safety, convenience, quick access to money, increased savings), which is the MOST compelling? Why?
Answers
Answer:
Step-by-step explanation:
There are 20 marbles in a bag. 16 are red. The remaining are white. What is the probability of selecting a red marble
Answers
20 Marbles Total
16 Red
16/20=.8=80%
Chase bought 5 chicken wings for $9.50. If Chase spent $26.60, how many chicken wings did he buy?
Please help me find the answer for this ( I think the answer is 14? I don't know for sure) thank you so much if you help me!
Answers
Find the price of 1 wing:
9.50 / 5 = 1.90 per wing
Divide total spent by price per wing:
26.60 / 1.90 = 14
Answer: 14
Answer:
14
Step-by-step explanation:
$9.50 / 5 = $1.90
$26.60 / $1.90 = 14
16. John's daily income is $120. His daily income is 20% more than Michael's daily income. What is Michael's
daily income?
Plz send step by step explanation
Will mark as a brainiest
Answers
Answer:
Michael's daily income is $96
Step-by-step explanation:
Given
john's income=$120
by question
John's income is 20%more than Micheal's
so,. Micheal's income= John's income - 20%of John's income
=$120 - 20%of $120
=$120 -20/100*$120
=$120 - $24
=$96
Answer:
100
Step-by-step explanation:
[tex]x + \frac{20x}{100} = 120 \\ x + \frac{x}{5} = 120 \\ 5x + x = 600 \\ 6x = 600 \\ x = 100[/tex]
Solve the equation for the y-value and choose whether it is a direct variation or inverse variation
xy = 7
Answers
Answer: Choice B
y = 7/x
inverse variation
=========================================================
Explanation:
We divide both sides by x to isolate y. That's how we go from xy = 7 to y = 7/x
This is an inverse variation because it's in the form y = k/x. The constant is k = 7.