Answer:
[tex]\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FactoringExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Product Rule: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
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]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[cos(u)] = -u'sin(u)[/tex]
eˣ Derivative: [tex]\displaystyle \frac{d}{dx}[e^u] = u'e^u[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{(3x + 1)cos(2x)}{e^{2x}}[/tex]
Step 2: Differentiate
[Derivative] Quotient Rule: [tex]\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - \frac{d}{dx}[e^{2x}](3x + 1)cos(2x)}{(e^{2x})^2}[/tex][Derivative] [Fraction - Numerator] eˣ derivative: [tex]\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{(e^{2x})^2}[/tex][Derivative] [Fraction - Denominator] Exponential Rule - Powering: [tex]\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}[/tex][Derivative] [Fraction - Numerator] Product Rule: [tex]\displaystyle y' = \frac{[\frac{d}{dx}[3x + 1]cos(2x) + \frac{d}{dx}[cos(2x)](3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}[/tex][Derivative] [Fraction - Numerator] [Brackets] Basic Power Rule: [tex]\displaystyle y' = \frac{[(1 \cdot 3x^{1 - 1})cos(2x) + \frac{d}{dx}[cos(2x)](3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}[/tex][Derivative] [Fraction - Numerator] [Brackets] (Parenthesis) Simplify: [tex]\displaystyle y' = \frac{[3cos(2x) + \frac{d}{dx}[cos(2x)](3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}[/tex][Derivative] [Fraction - Numerator] [Brackets] Trig derivative: [tex]\displaystyle y' = \frac{[3cos(2x) -2sin(2x)(3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}[/tex][Derivative] [Fraction - Numerator] Factor: [tex]\displaystyle y' = \frac{e^{2x}[(3cos(2x) -2sin(2x)(3x + 1)) - 2(3x + 1)cos(2x)]}{e^{4x}}[/tex][Derivative] [Fraction] Simplify [Exponential Rule - Dividing]: [tex]\displaystyle y' = \frac{3cos(2x) -2sin(2x)(3x + 1) - 2(3x + 1)cos(2x)}{e^{2x}}[/tex][Derivative] [Fraction - Numerator] Factor: [tex]\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}[/tex]Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e
Four coordinates A, B, C and D form a rectangle.
A = (2,8), B = (9, 2) and C'=(2, 2)
What are the coordinates of D?
Which of the following pairs of ratios are equivalent?
1) 38 : 133 and 16 : 56 , 2) 15 : 20 and 28 : 56
Answer:
38 : 133 and 16 : 56 are equivalent
Step-by-step explanation:
Given
1) [tex]38 : 133[/tex] and [tex]16 : 56[/tex]
2) [tex]15 : 20[/tex] and [tex]28 : 56[/tex]
Required
Determine which is equivalent
1) [tex]38 : 133[/tex] and [tex]16 : 56[/tex]
[tex]Ratio = 38 : 133[/tex]
Divide by 19
[tex]Ratio = 2:7[/tex] --- can't be further simplified
[tex]Ratio = 16 : 56[/tex]
Divide by 8
[tex]Ratio = 2:7[/tex]
Hence:
[tex]38 : 133[/tex] and [tex]16 : 56[/tex] are equivalent
2) [tex]15 : 20[/tex] and [tex]28 : 56[/tex]
[tex]Ratio = 15 : 20[/tex]
Divide by 5
[tex]Ratio = 3 : 4[/tex]
[tex]Ratio = 28 : 56[/tex]
Divide by 28
[tex]Ratio = 1:2[/tex]
Hence, both are not equivalent.
B. Subtract the following integers
16.9 - (-5) =
17. - 12 - ( + 8) =
18. 15 - 9=
19. - 5 - (-8)=
20. - 11 - ( + 14 ) =
Answer:
16. 9 - (-5) = 21.9
17. -12 - ( + 8) = -4
18. 15 - 9 = 6
19. -5 - (-8)= 3
20. -11 - ( + 14 ) = -25
Step-by-step explanation:
Subtracting a negative from another number is the same as adding the number. Thus, 16.9 - (-5) = 16.9 + 5.
Hope it helps <3 :)
Answer:
16.9-(-5)=21.9
17.-12-(+8)= -3
18.15-9=9.15
19.-5-(-8)=22
20.-11-(+14)=-5
(06.04 HC) The graph shows Wilson's science scores versus the number of hours spent doing science homework. A graph titled Wilsons Science Scores shows Hours of Practice in a Week on x axis and Science Scores on y axis. The x axis scale is shown from 0 to 5 at increments of 1, and the y axis scale is shown from 0 to 50 at increments of 5.The ordered pairs 0, 15 and 0.5, 18 and 1, 18 and 1.5, 25 and 2, 30 and 2.5, 35 and 3, 40 and 3.5, 43 and 4, 41 and 4.5, 45 and 5, 48 are shown on the graph. A straight line joins the ordered pairs 0, 14.9 and 5, 50. What will most likely be Wilson's approximate science score if he does science homework for 6 hours a week? (5 points) Group of answer choices 33 points 42 points 52 points 55 points
Answer:
The answer 55
Step-by-step explanation:
Because it goes up by five for they gave us the amount of point they get for 5 hours and the amount of point he had for 5 hours was 50 so we just needed to add 5 more and 50+5= 55
I don't know if I made myself clear but good luck! :)
Answer
Personally I think it's 55 as well!
Step-by-step explanation:
Good luck! :)))
1 of 12
Eli is following this recipe to bake bread rolls.
He uses 500 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
400 g flour
6 g salt
8 g yeast
40 mL oil
360 ml water
g salt
g yeast
mL oil
mL water
Answer:
360
Step-by-step explanation:
&$5%4645$655$456&&&66
Luke's family goes to the movies and purchase a large popcorn. They are are debating whether or not to purchase any drinks.The table below shows how much they'll spend based on the number of drinks they decide to purchase
Answer:
where is the picture to show ????
Answer:
x=9/4
Step-by-step explanation:
If you have a cylinder with a volume of 282.6 ft3 and a cone with a congruent radius and height. What is the volume of the cone
The volume of a cone is 1/3 the volume of a cylinder with congruent dimensions, so:
286.6 / 3 = 95.53333... ft3
In the year 2001, a person bought a new car for $15500. For each consecutive year after that, the value of the car depreciated by 5%. How much would the car be worth in the year 2005, to the nearest hundred dollars?
Answer:
$12,000.
Step-by-step explanation:
Given that in the year 2001, a person bought a new car for $ 15500, and for each consecutive year after that, the value of the car depreciated by 5%, to determine how much would the car be worth in the year 2005, to the nearest hundred dollars, the following calculation must be performed:
100-5 = 95
15,500 x 0.95 x 0.95 x 0.95 x 0.95 x 0.95 = X
14.725 x 0.95 x 0.95 x 0.95 x 0.95 = X
13,988.75 x 0.95 x 0.95 x 0.95 = X
13,289.3125 x 0.95 x 0.95 = X
12,624.846875 x 0.95 = X
11.993.60453125 = X
Thus, to the nearest hundred dollars, the cost of the car after 5 years will be $ 12,000.
Find the slope. (10,-6) and (13,-7)
Answer:
-1/13
Step-by-step explanation:
i did it
pls help quickly maath
Answer:
It should be A
Step-by-step explanation:
Since it is asking for the squares to circles, it is not option c. B is also incorrect because the ratio is not correct, which leaves the only answer to be A.
The endpoints of two radii that touch the circle become the endpoints of a section of the circle. What is the curved section between the endpoints called?
A radius
B diameter
C chord
D arc
Answer:
It is a cord
Step-by-step explanation:
i just took the quiz and got it right :)
Answer:
D. arc
Step-by-step explanation:
everyone keeps saying its "chord" but I tried that and I got it wrong...
PLZ HELP!! I NEED QUICKLY!!
Choose 5 ordered pairs whose first and second coordinate are equal. Plot these points and connect them. What kind of figure do you get? In what quadrants does the figure lie?
Answer:
no worries about the other day and I had literally forgotten about the other night and was just so I could tell me how I felt and I had a flat rate that you and I had a
The figure of y = x will be a straight line with slope 1 and they ;lie in the first quadrant and the third quadrant.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.
We have to choose 5 ordered pairs first whose first and second coordinate are equal.
Let the coordinates be (-4, -4), (-2, -2), (0, 0), (2, 2) and (4, 4).
The ordered pairs are of the form (x, x), that both the coordinates have same value.
So we get a linear function y = x
The graph of a linear function will be a straight line.
Since y = x, the graph will be a straight line which tends to the positive direction and the slope of the line = 1.
That is , the angle that the line making with the X axis is 45°.
And the figure lies on first and third quadrant.
Hence the figure of y = x would be a straight line with slope 1.
To learn more about Linear Functions, click :
https://brainly.com/question/21107621
#SPJ2
Jeff had 20 $ he spent 1/8 on his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left
Answer:
9.50$
Step-by-step explanation:
First, multiply 20 by the given fractions
20*1/8=2.5
20*2/5=8
Add the two together to get the total amount of money Jeff spent, 10.5, then subtract 10.5 from 20 to get the total amount he has left, 9.5
Answer:
$9.50
I did a test with this question and the correct answer was 9.50
Rachelle bought x pounds of fruit for
$2 per pound and a gallon of milk for
$3.79. She spent a total of $17.29. Write
an equation that can be used to find
how many pounds of fruit she bought.
Step-by-step explanation:
step 1. 2x + 3.79 = 17.29. this is the answer.
Find angle. Picture below!
Answer:
m<QRP=42degrees
m<Q=79degrees
m<P=59degrees
Step-by-step explanation:
What is the area of this parallelogram
Answer:
B. 12.25
Step-by-step explanation:
A=bxh=3.5·3.5=12.25
Answer:
17.15
Step-by-step explanation:
There are 2 ways to solve this.
One way is this:
Add 1.4 and 3.5 together to get the total length of the parallelogram. The sum would be 4.9. Then multiply this number by the height of the figure(3.5cm). So that the product of 4.9 and 3.5 is 17.15.
The second way is this:
Find the area of the two triangles and the square and then add those products together. So add:
1.4 x 3.5 ÷21.4 x 3.5 ÷23.5 x 3.5So solve this equation and you will get:
2.45 + 2.45 + 12.25=17.15Test is due Wednesday and I need urgent help. I will give good review!
Answer:
B and D
Step-by-step explanation:
Answer:
b and d
Step-by-step explanation:
Find the surface area for a sphere with a radius of 10 feet. Round to the nearest whole number.
A.1.256
B.4.189
C.1,089
D.1,568
Answer:
C is my answer
Thank You
Mark me as Brainilest Answer please ty
Sam says: 9.05kg is equal to 9500g. Is he right or wrong? Explain your answer.
Answer:
Step-by-step explanation:
Sam is wrong because 9,05 kg =9050g which is different to 9500g
Answer:
wrong 1 kilo in a gram is 1000 so u just going to add 1 zero on the back so 905+0= 9050 grams
kate pays $203 in advance on her account at the athletic club. Each time she uses the club, $9 is deducted from the account. Find the remaining in the account after 12 visits
Answer:
95
Step-by-step explanation:
The equation to solving this would be 203 - (9 multiply 12). If you multiply 9 and 12 you get 108. Minus 108 from 203 and you get 95.
help me please i will give brainliest and excellent and thank you
math
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
1) know your grams and centigrams!
1 Grams = 100 Centigrams
2) If you want to find the centigrams, all you gotta do is; multiply the gram to 100.
For example: This bar of chocolate has 100 grams of sugar. I wonder what is the mass in centigrams?
100 grams * 100 centigrams = 1,000 Centigrams.
3) To answer your question; multiply 347 by 100!
347 * 100 = 34,700 centigrams.
Hope this helps!
Find the area of the triangle
Answer:
[tex]\sqrt{20}\ or\ 2\sqrt{5}[/tex]
Step-by-step explanation:
Please give me an answer with an explanation.
Answer:
40 and 10
Step-by-step explanation:
1. if the length is 'l' and height is 'h', then according to the condition 1/4*l=h.
2. if the given area is 400, it means, h*l=400;
3. if to substitute h=1/4*l into the formula of the area, then
l*l*1/4=400; ⇔ 1/4*l²=400;
4. if to calculate the value of the 'l', then l=40 (the required length).
5. if to substitute l=40 into 1/4*l=h, then h=10 (the required height).
Hi can someone please answer and explain all you work thank you! I’ll mark brainliest
Does the graph below represent a function?
yes
no
sometimes
not enough information
Answer:
yes it does represent a function.
Step-by-step explanation:
In the image shown line n is a transversal cutting parallel lines l and m
A- 79
B- 81
C- 83
D- 86
the answer to your question is C
Jenny earns $30 a day working part time at a supermarket. Write an expression to represent the amount of money she will earn in d days.
Answer: d($30)
Explanation: $30 times d which d is the number of days.
Expresa el área del cuadrado interno con un polinomio,luego calcula el área
x = 4y y = 10.
Es para hoy ayudaaaaaa
Answer:
si me ayudas diciéndome de qué materia es y qué grado eres Y qué página es Con gusto te ayudo pero si no es de quinto grado página 83 y 82 del trimestre 1 de la guía tal vez no te lo pueda responder pero te envió una foto para que veas Sí sí es lo que estás buscando o no
what is the solution to the equation sqrt 2x+3- sqrt x+2=2
Answer:
x= 23
Step-by-step explanation:
The correct answer on edge is 23
Please help ASAP if you know how. Thanks so much
Answer:
B) -6.61, 0.61
Step-by-step explanation:
Answer obtained by graphing the formula.
