Answers
Answer:
[tex]y'= \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Step-by-step explanation:
We have [tex]e^{2x} = \ln(y^3)[/tex] and we want the implicit differentiation [tex]\dfrac{dy}{dx}f(x) = y'[/tex]
Therefore, we want to separate the [tex]y[/tex] from the equation.
[tex]\ln(y^3) =e^{2x} \implies 3 \ln(y) = e^{2x} \implies \ln(y) = \dfrac{e^{2x} }{3}[/tex]
[tex]\implies e^{\ln(y)} = e^{e^{2x}/3} \implies \boxed{y = e^{e^{2x}/3}}[/tex]
Now we can calculate the derivative. By the chain rule,
[tex]y' = \dfrac{d}{dx}\left(e^{e^{2x}/3}\right) = e^{e^{2x}/3}\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right)[/tex]
Now
[tex]\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right) =\dfrac{1}{3}\dfrac{d}{dx}\left(e^{2x}\right) = \dfrac{2}{3}e^{2x}[/tex]
Therefore
[tex]y' = e^{e^{2x}/3}\cdot \dfrac{2}{3}e^{2x} = \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Related Questions
heyyyyyyyyyyyyyyyyyyyyyyy
Answers
Answer:
Step-by-step explanation:
The aquarium has 3 more yellow fish than green fish. 60% of the fish are yellow. How many green fish are in the aquarium?
Answers
Find the length x…..
Answers
Answer:
x = 4
Step-by-step explanation:
6 : 4.5 = 4 : 3
x : 3 = 4: 3
x= 4
I'll give brainliest to the right answer!!!
Find three consecutive odd integers such that the difference of twice the second and the first is 11.
Answers
Answer:
7, 9, 11
Step-by-step explanation:
question: Find three consecutive odd integers such that the difference of twice the second and the first is 11.
make the 3 consecutive odd intergers x, y, and z.
numbers are consective (come right after another) AND odd, meaning you would add 2 every time. therefore:
x+2=y
y+2=z
given that: "difference of twice the second and the first is 11."
difference means subtraction
second number is the variable y
first number is the variable x
2y-x=11
----------------
3 equations:
2y-x=11
x+2=y
y+2=z
----------solve by substitution
x+2=y
x =y-2 into 2y-x=11
2y-(y-2)=11
2y-y+2=11
y=9
second number is 9
-----
numbers are 7, 9, 11
Find the points on x^2+3(y-2)^2 = 27
which are closest to and farthest from the origin
Answers
[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.
Let be a curve of the form [tex]x^{2}+3\cdot (y-2)^{2} = 27[/tex]. The distance with respect to origin is found by using the following Pythagorean identity:
[tex]r = x^{2}+y^{2}[/tex] (1)
Where [tex]r[/tex] is the square distance function.
We can modify (1) as following:
[tex]r = [27-3\cdot (y-2)^{2}]+y^{2}[/tex]
[tex]r = 27-3\cdot (y^{2}-4\cdot y +4)+y^{2}[/tex]
[tex]r = 27-3\cdot y^{2}+12\cdot y -12 + y^{2}[/tex]
[tex]r = -2\cdot y^{2}+12\cdot y+27[/tex] (1b)
Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:
First derivative test
[tex]-4\cdot y +12 = 0[/tex]
[tex]y = 3[/tex]
Second derivative test
[tex]r'' = -4[/tex]
The y-component represents a maximum.
Now we graph the function with the ressource of a graphing tool, we find the following points:
Farthest points: [tex](-4.89, 3)[/tex], [tex](4.89, 3)[/tex].
Closest points: [tex](0, -1)[/tex].
[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.
To learn more on ellipses, we kindly invite to check this verified question: https://brainly.com/question/19507943
Population grows.
The population of Boston, MA in 2019 was
692,600 people with an annual rate of increase
1.4%. In what year the population of Boston
will reach 1,000,000 people, if the grows rate
stays the same? The function describing
population grows is P(x)=692,600 - 1.014,
where x is number of years.
Answers
Population are often modelled by exponential functions
The population will reach 1000000 people after 26.5 years
The population function is given as:
[tex]P(x) = 692600 \times 1.014^x[/tex]
When the population reaches 1000000 people, we have:
P(x) = 1000000
So, the equation becomes
[tex]1000000 = 692600 \times 1.014^x[/tex]
Divide both sides by 692600
[tex]1.444=1.014^x[/tex]
Take logarithm of both sides
[tex]log(1.444)=log(1.014)^x[/tex]
Apply logarithm to both sides
[tex]log(1.444)=xlog(1.014)[/tex]
Make x the subject
[tex]x = \frac{log(1.444)}{log(1.014)}[/tex]
Solve the logarithms of 1.444 and 1.014
[tex]x = \frac{0.15957}{0.00603}[/tex]
Divide
[tex]x = 26.5[/tex]
The value of x, is the number of years the population reaches 1000000 people.
Hence, the population will reach 1000000 people after 26.5 years
Read more about population at:
https://brainly.com/question/24581924
Beatrice watched two films at the theatre. The first she watched was 2 1/6 hours long and the second film was 1 5/6 hours long . Calculate the total length of the two films
Answers
Answer:
4 Hours
Step-by-step explanation:
2 1/6 = 13/6
1 5/6 = 11/6
13/6+11/6= 24/6
Simplify 24/6 which will give you 4
Approximately what portion of the box is shaded blue?
Answers
Answer:
1/2 approximately 1/2......
Answer: C. (1/2)
Step-by-step explanation: You can see they split the box into 2 halves and one half is shaded so 1/2 is shaded you can also solve by 2/2 - 1/2 = 1/2
3.
Which two expressions can be used to find the value of (36)(24)?
A (30-6)(30 - 6)
(30 + 6)(30 - 6)
C 30²- 6²
B
D302 - 360 +62
-
E 30² +62
Answers
Answer:
962
Step-by-step explanation: 30²- 6² is 962
A B C or D? please help
Answers
Answer:
(x-1) and (x-5)
Step-by-step explanation:
option a .......
USE THE DIATRIBUTIVE PROPERTY TO WRITE 6(W=5) AS AN EQUIVALENT EXPRESSION
Answers
answer ?
30 or 30W
Step-by-step explanation:
this isn't a real equation. you can't have an equal sign inside a parentheses but assuming that the question is 6(W) and W equals 5, we can substitute the 5 and distribute the 6 to get 6x5 = 30
hlep me plsssssssssssssssssssssssss
Answers
{(-1, -3),(0,-1),(1,1),(2,3),(3,5)}
Answer:
B.
Step-by-step explanation:
It is not A because it does not make sense and does not match up.
It Is not C because that is just points and it is asking for a function.
D is wrong.
So It is B.
Here is the graph for B. It matches up.
[tex]\mathrm{Axis\:interception\:points\:of}\:2x-1:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{2},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-1\right)[/tex]
[tex]\mathrm{Slope\:of\:}2x-1:\quad m=2[/tex]
How many 3/5 s are in 5?
Answers
Answer:
none , its 2 2/5
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
it will be 3 because 4 3/5`s is 2 and 2/5 and 3 3/5`s is 1 and 4/5 hope that helped your question.
A random variable x has a mean of 22 and a standard deviation of 3.1. Random samples of size 40 are drawn, and the sample mean calculated each time. What is the probability that, for a given sample, is 21?
Answers
in this question, we are given the poverty function Our X equals no point to for X equals not 123 on before. So we are asked to find the mean and standard deviation. So the first step is to dio our property distribution tables. We are no one to hey wonderful. When we get told, it's no point to went to Teoh went to and not point to stuff. It's nice and easy. The next room we need to do is X he exit. We're gonna times are probability of X which is not 20 for all of them and by the value of X itself. So for the 1st 1 we're times in nor point to buy zero So we get zero 2nd 1 time to North point to buy one which is no point to no no point to about two, which is full no point you by three which is six and no 60.2 times four which is ain't on Then the way we get the main is to some all these together. So every animal together we get to not to is me which is on me I'm just gonna put less some of X P x is a reminder of how we got that. So if we do total so the next thing we need to dio is doomed. Ex spread P X so x zero squared is still zero and zero times. Anything is zero once where it is still one so that times not point to a store not point to. But now two squared is four of four times no point to there's no 0.8 three squared is nine. So no 90.2 times nine is now. One point ain't on four spread is 16 so one out of the North Point to buy 16 which is 3.2 on the total for that is not quick to note. 0.8 plus 1.8 plus 3.2, which gives us six. So we now need ah variation, which is the expectation of X. It's what, which is this Butthead and we need to take from that expectation of X, which is our mean squared same. We're looking at six minus to squared. So that's six minus four, which is to on to get the standard deviation. We just need to do root off answer. So If we do, son deviation equal root of Arians equals route to Ruutu is actually an irrational number. So it will just keep going forever. So we'll just simplify to one distal place, which is 1.4. So they haven't you mean is too on the standard deviation is 1.4.
Little help please...?
Answers
Answer: The answer is B
Step-by-step explanation:
It's B because every pound is $14 and for C it looks similar, until you add another pound and then option B becomes $28 per 2 pounds and option C becomes $25 per 2 pounds. Therefore, the answer is B
The temperature was -1°F at noon and dropped to -14°F by the evening.
What was the change in temperature?
13°F
-13°F
-15°F
15°F
Answers
Answer:
-13°F is the change in temperature.
Step-by-step explanation:
The change in temperature is,
→ -1 + x = -14
→ x = -14 + 1
→ [ x = -13 ]
Hence, -13°F is the change.
This 3 by 3 grid shows nine 1 cm x 1cm squares and uses 24 cm of wire.
What length of wire is required for a similar 20 by 20 grid?
A 400 cm B 420 cm C 441 cm D 800 cm E 840 cm
Answers
Answer:
E 840 cm
Step-by-step explanation:
For a 20×20 grid, there will be 21 strands in the vertical direction, and 21 in the horizontal direction. Each strand wil be 20 cm long. The total length is ...
(20 cm)(2 × 21) = 840 cm
_____
Additional comment
In this case, we take "similar" to mean that the grid squares are 1 cm, and the wire encloses a larger array of those squares.
In geometry, the term "similar" would mean the larger grid is simply a scaled-up version of the smaller one, with squares that are 20/3 cm, instead of 1 cm. The length of wire required in that case is (4+4)(20 cm) = 160 cm = (20/3)×(24 cm).
Devon has $900 in a savings account. The interest rate is 7% per year and is not
compounded. How much interest will she earn in 2 years?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and t is the time in years.
=
Answers
Answer:
$ 12600
Step-by-step explanation:
According to the question, you have to find the simple interest that Devon earn after 2 years,
You can use this formula to find that.
I = P r tHere,
P = principal ( $ 900)
r = rate ( 7%)
t = time ( 2 years)
Let us solve now.
I = p × r × t
= $ 900 × 7% × 2 years
= 6300 × 2
= $ 12600
Hope this helps you.
Let me know if you have any other questions :-)
Please hurry!! This assignment is almost due thank you!!
Answers
Answer:
x = 33
Step-by-step explanation:
(x-17)°+(5x-1)°=180°
6x-18 = 180
6x = 198
x = 33
6) Solve
5x < -10
AX <-2
B) x>-2
CXC-15
D) x < -50
Answers
Hey there!
5x < -10
DIVIDE 5 to BOTH SIDES
5x/5 < -10/5
CANCEL out: 5/5 because it gives you 1
KEEP: -10/5 because it helps solve for the x-value
NEW EQUATION: x < -10/5
SIMPLIFY IT!
x < -2
It is an OPEN circle shaded to the RIGHT
Therefore, your answer should be:
Option A. x < -2
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
6x + ____ = 10 Please find the blank.
Answers
Answer:
6x +4=10
I think this is answer
Three boxes are stacked one on top of the other. One box is 4 feet 8 inches tall, one is 3 feet 10 inches tall, and one is 2 feet 7 inches tall. How high is the stack?
Write your answer in feet and inches. Use a number less than 12 for inches.
Answers
what is 10+10...........................
Answers
Answer:
that would be 20 lol
Step-by-step explanation:
Which sizes can he display? Choose all that apply.
linch
4
0.5 inch
3 inch
8
1 inch
1.5 inch
Answers
Step-by-step explanation:
He can choose the dispay boxes that are 0.5 in, 1/4 in, and 3/8 in
Hope this helps
May I get braineist pls?
!!!!!!!!!HELP I need asnwer ASAP
Answers
1) 2, 8
2) 2, 1/2
مل
Amy is adding two numbers. She got the answer
which is 2003 However she copied the question wrong.
The one's column of the first number should be 7. she
wrote it to I. The hundred's column
of
the second number
should be 2. she wrote it to 3. What is the correct ansuel
if she copied it correctly?
Answers
Answer:
2999
Step-by-step explanation:
There's a lot of possibilities bc it didn't mention any tens columns.
I’m having trouble with this question I need some help please
Answers
Answer:
[tex] \frac{1}{2} \: \: \: \: \: \frac{1}{4 \: } \: \: \: \frac{1}{8} [/tex]
[tex] \frac{4}{8} \: \: \: \frac{2}{8} \: \: \: \frac{1}{8} [/tex]
She ate
[tex] \frac{7}{8} [/tex]
can someone please help me
Answers
Answer:
The mode is 31
good luck naka
solve this: 23.769km-----?-----m
Answers
1 km = 1000 m, so:
23,769 km = 23,769 · 1000 m = 23 769 m
Answer:
23769m
Step-by-step explanation:
Basicly, 3.769x 1000= 23769m
Please mark brainliest
What is the slope of the line?
Answers
Answer:
-3/4
Step-by-step explanation: