The derivative for [tex]y=eu(x)[/tex]; [tex]u(x)[/tex] is a function in terms of [tex]x[/tex] is [tex]\frac{dy}{dx}[/tex]=[tex]eu'(x)[/tex]+ [tex]u(x)e[/tex].
Definition of derivative-A derivative is the rate of change of a function with respect to a certain variable . Derivatives are fundamental to the solution of problems in calculus and differential equations.
There are certain rules of differentiation which help us to evaluate the derivatives of some particular functions. :
Power Rule.
Sum and Difference Rule.
Product Rule.
Quotient Rule.
Chain Rule.
Given: [tex]y=eu(x)[/tex]
Explanation:-This equation can be solved using the product rule of derivatives .
According to the product rule derivative of uv will be taken as -
u(v)' + v(u)'
where (') represents derivative of the variable.
Therefore accordingly, [tex]y=eu(x)[/tex]
Differentiating with respect to [tex]x[/tex],
[tex]\frac{dy}{dx} =e(u(x))'+u(x)(e')[/tex]
[tex]\frac{dy}{dx} =eu'(x)+u(x)e[/tex]
So, finally the derivative of the function in terms of x is [tex]\frac{dy}{dx}[/tex] = [tex]eu'(x)+[/tex][tex]u(x)e[/tex]
To learn more about derivatives, visit:
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Simplify the expression by combining like terms.
Write the terms from the highest to the lowest
power of the variable.
Answer:
19y² - 6y - 8
Step-by-step explanation:
4y² + y² - 3y - 6 + 14y² - 2 + 4y - 7y
4y² + y² + 14y² - 3y + 4y - 7y - 6 - 2
19y² - 6y - 8
Answer:
19^2-6y-8
Step-by-step explanation:
4y^2+y^2-3y-6+14y^2+4y-7y
4y^2+y^2+14y^2-3y+4y-7y-b-2
Answer: 19y^2-6y-8
Hope it helps....
Have a great day!! :)
How do you write 8.317 x 10^6 in standard form?
Answer:
[tex]8,317,000[/tex]
Step-by-step explanation:
[tex]8.317\times10^6[/tex]
Rewrite 10^6:
[tex]10\times10\times10\times10\times10\times10[/tex]
Solve:
[tex]8.317\times(10\times10\times10\times10\times10\times10)\\=8,317,000[/tex]
8,317,000 is your final answer!
GUYS ANYONE HERE I REALLY NEED HELP PLS! Find the area of the polygon with vertices D (-1, 2), E (2, 2), F (2, -1), and G (-3, -1). If necessary, round to the nearest tenth
Answer:
48 units
Step-by-step explanation:
1. graph
2. separate into a triangle and a square
3. the square is 6x6 squares, so 36 there
4. the triangle is 4x6, so (4x6)/2 is 12
5. 36+12 = 48 units
Find the volume of the cylinder. Leave your
answer in terms of pi.
8 cm.
8 cm.
Question 5 1 To get from my home to my school, I travel approximately 4.1 miles east, then approximately 4.7 miles north. What is the approximate distance from my home to my school, rounded to the nearest tenth of a mile? * School Distance Home 90°
Answer:
I hope you find the answer
Match the graph to its equation.
Answer: First one is A, 2nd one is B, 3rd one is C
Step-by-step explanation:
Please help!! Brainlyest!!
someone please help me
Answer:
Ok it might take a bit but I'll help:))
Step-by-step explanation:
Solve the following
5x20
Answer:
100
Step-by-step explanation:
1
20
X 5
100
Diana is throwing a ball across a 56-yard field she threw it 3/4 of the way across the field how far did diana throw the ball?
Answer:
71
Step-by-step explanation:
which table represents y as a function of x
HEYYYY YOU YEA YOU!!!
whoever can come up with the best sentence to relate to this will get BRAINLIEST
Who here is sad because they hate school and school gives them depression because of the amount of work and because they are tired of seeing idiots around them and their whole existence just annoys you and sometimes you even imagine yourself running them over with a bus because they cant comprehend the fact that you just want them to rot in hell for all eternity for example they could just breath and then you give them the "stank look".....or is it just me....its not just me right?????
Answer:
I think that school is somewhat fun, now it is just straight up boring, and yeah sometimes I feel like there are not smart people, and there are weird people, so annoying, I wish they aren't there a lot, but hey, if you can, listen to music, and maybe make some time to do what you like so you can forget about school for a little and relieve your stressssss
if a triangle is dilated with a scale factor of 3, how do the sizes for the pre-image and image compare?
Answer:
Please check explanations
Step-by-step explanation:
When we dilate a particular figure, we are simply increasing the dimensions of its sides
By dilating the pre-image by a factor of 3, we are simply increasing the dimensions of it by a multiple of 3
so say for example, the base of the pre-image has a measure of 4 ft, the base of the image which is the pre-image dilated by a scale factor of 3 will be 4 ft * 3 = 12 ft
What this mean is that we have succeeded in tripling the dimension of the pre-image to give the dimension of the image
8-7 test prep (will give brainliest!!!)
Answer54: A, 55: G, 56: D
Step-by-step explanation:
Answer:
54. 2cm
55. between 6 and 7
56. two irrational numbers
Step-by-step explanation:
Help!! Il give you brainlest
Answer:
ithink the first one :p
Step-by-step explanation:
Plss I need this answer....pls help me. Explain this question and answer it.
Answer:
Figure three is the odd one out
Step-by-step explanation:
it is different from the other figures. The other figures are all the same, they're just rotated. Figure three is different from all of them though
68 less than 55 times a number is equal to the number.
I will make brainliest
Answer:
5x - 68 = x
Step-by-step explanation:
number = x
5x - 68 = x
Solve for x:
5x - 68 = x
-68 = x - 5x
-68 = -4x
68 = 4x
x = 68/4
x = 17
Answer:
55x-68 = x
Step-by-step explanation:
Please help, 15 points
Answer:
The answer is 10.
Step-by-step explanation:
The equation you are given is in slope-intercept form or y=mx+b where m is the slope and b is the y intercept. Your equation is y=10x, so the slope or m is 10.
Mitch is making some bread dough. To make the bread dough, Mitch uses 5 1/2 cups of wheat flour, 1 3/4 cups of rice flour, and 2/3 cup of white flour. How many cups of flour, in total, does Mitch use? Show or explain all your work.
Answer: 7 11/12 cups of flour
Step-by-step explanation:
The number of cups of flour in total that Mitch uses will be gotten by adding the values for the cups for each type of flour that's used. This will be:
= 5 ½ + 1¾ + ⅔
= 5 6/12 + 1 9/12 + 8/12
= 6 23/12
= 6 + 1 11/12
= 7 11/12 cups of flour
What is the total of club seats? If club seats are
8% of the total? and total is 5,000
please help!
Answer:
From what i've understood the answer is 400
Step-by-step explanation:
I have to graph these. I don't understand!!! please just tell me if it's a closed circle and where I have to put it
Answer:
Okay so im gonna put the pictures here, it might look like spam but i promise you its not
Step-by-step explanation:
The numbers are in order from x > 7 to x < 2
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
Help this is due in 2 minutes
Answer:
The percentage change each year is 2%
Step-by-step explanation:
Generally, we can have an exponential equation written as;
f(t) = I( 1 + r)^t
where f(t) is the value at a certain time
I is the initial value at t = 0
r is the growth rate
t is the time we are looking at
Thus, we have it that;
1.02 = 1 + r
r = 1.02 -1
r = 0.02
So, let us write 0.02 as a percentage
We have this as 2/100 which is the same as 2%
The percentage change each year is 2%
Please help
40 points
Answer:
44.11
Step-by-step explanation:
you can use SOH-CAH-TOA to find the answer.
T has adjacent and hypotenuse shown in the figure.
thus you can write it as,
[tex]cos(x) = 28 \div 39[/tex]
[tex]x = cos^{ - 1} (28 \div 39)[/tex]
[tex]x = 44.11[/tex]
(you can round the answer differently )
What is the length of C'D'?
Answer:
C'D
Step-by-step explanation:
3 1 half plus 1 half .. and haii
Determine the value of x. Round answer to the nearest hundredth. thank you to whoever helps! Will Be Marked as BRAINLIEST!
Answer:
34.61Step-by-step explanation:
Find the diagram attached
From the diagram;
Hypotenuse = 81.9
Angle of elevation = 65degrees
Required
The value of x (Adjacent)
Using the SOH CAH TOA identity
cos theta = adjacent/Hypotenuse
cos 65 = x/81.9
x = 81.9cos65
x = 81.9(0.4226)
x = 34.61
Hence the value of x to the nearest hundredth is 34.61
How far the penguin can walk in 1 second
Not known. This varies because it depends on if the penguin is going full speed or not, and the size or even just the penguin itself because not all penguins walk the same speed.
Answer:
1 step? what speed?
matt and anglela have 40$ together angela has 5more$ than matt how much
money does matt have
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
X=3
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Find the perimeter of the object
Help step by step please!
Answer:
29.42 units
Step-by-step explanation:
1) Find the perimeter around the semi-circle
To do this, we find the circumference of the circle using the given diameter:
[tex]C=\pi d[/tex] where d is the diameter
Plug in 6 as the diameter
[tex]C=\pi (6)\\C=6\pi[/tex]
Divide the circumference by 2
[tex]\frac{6\pi }{2} \\= 3\pi[/tex]
Therefore, the perimeter around the semi-circle is 3π units.
2) Find the perimeter around the rest of the shape
Although it's impossible to determine the lengths of the varied sides on the right side of the shape, we know that all of those vertical sides facing the right add up to 6. We also know that all of those horizontal sides facing up add up to 7. Please refer to the attached images.
Therefore, we add the following:
7+6+7
= 20
Therefore, the perimeter around that area of the shape is 20 units.
3) Add the perimeter around the semi-circle and the perimeter around the rest of the shape
[tex]20+3\pi \\= 20+9.42\\= 29.42[/tex]
Therefore, the perimeter of the shape is approximately 29.42 units.
I hope this helps!
Aaron bought a stereo system for $55 and spends $8.45 on parts. He sells the system for
$60. What is his profit/loss?
Answer:
his loss is $3.45
Step-by-step explanation:
you just add then subtract