Answers
Answer:
[tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}[/tex]
[tex]\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Calculus
Derivatives
Derivative Notation
eˣ Derivative: [tex]\displaystyle \frac{d}{dx}[e^x] = e^x[/tex]
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x \cdot e^x][/tex]
[tex]\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x \cdot e^{2x}][/tex]
Step 2: Differentiate
[tex]\displaystyle \frac{d}{dx}[e^{2x}][/tex]
[Derivative] Product Rule: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x]e^x + e^x\frac{d}{dx}[e^x][/tex][Derivative] eˣ Derivative: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = e^x \cdot e^x + e^x \cdot e^x[/tex][Derivative] Multiply [Exponential Rule - Multiplying]: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = e^{2x} + e^{2x}[/tex][Derivative] Combine like terms [Addition]: [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}[/tex][tex]\displaystyle \frac{d}{dx}[e^{3x}][/tex]
[Derivative] Product Rule: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x]e^{2x} + e^x\frac{d}{dx}[e^{2x}][/tex][Derivative] eˣ Derivatives: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = e^x(e^{2x}) + e^x(2e^{2x})[/tex][Derivative] Multiply [Exponential Rule - Multiplying]: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = e^{3x} + 2e^{3x}[/tex][Derivative] Combine like terms [Addition]: [tex]\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Related Questions
Determine the equation of circle A.
(x - 1)2 + (y + 2)2 = 9
(x + 1)2 + (y-2)2 = 9
(x-1)2 + (y + 2)2 = 3
(x + 1)2 + (y-2) = 3
Answers
I'm not sure but if you have photomath or Microsoft mathematics use it to solve your problem
what is x ? full explanation please
Answers
Answer:
x = 6
Step-by-step explanation:
Looking at the figure, we can say that it is a vertical angle.
5x - 7 = 23
5x - 7 + 7 = 23 + 7
5x = 30
5x / 5 = 30 / 5
x = 6
Since it is a vertical angle, the other side should be 23⁰. You can also plug in the x value to find if it gives you 23⁰ or not.
5x - 7
5(6) - 7
30 - 7
23
Therefore, x = 6. Hope this helps and stay safe, happy, and healthy, thank you :) !!
In an arithmetic sequence Sn=n^2SN=N^2-2N .USE formula (Tn=Sn-Sn-1) to determine the value of Tn
Answers
Answer:
[tex]T_n = 2n -3[/tex]
Step-by-step explanation:
Given
[tex]S_n = n^2- 2n[/tex]
[tex]T_n = S_n - S_{n-1[/tex]
Required
Find [tex]T_n[/tex]
[tex]S_n = n^2- 2n[/tex]
Calculate [tex]S_{n-1[/tex]
[tex]S_{n-1} = (n-1)^2- 2(n-1)[/tex]
[tex]S_{n-1} = n^2-2n+1- 2n+2[/tex]
[tex]S_{n-1} = n^2-2n- 2n+1+2[/tex]
[tex]S_{n-1} = n^2-4n+3[/tex]
[tex]T_n = S_n - S_{n-1[/tex] becomes
[tex]T_n = n^2 - 2n - (n^2 - 4n +3)[/tex]
[tex]T_n = n^2 - 2n - n^2 + 4n -3[/tex]
[tex]T_n = n^2 - n^2- 2n + 4n -3[/tex]
[tex]T_n = 2n -3[/tex]
OMG PLEASE HELP MEEEEEEE
Which expression could represent the additive inverse property?
A) −9 + 0
B) −9 −9
C) −9 + 1
D) −9 + 9
Answers
So the answer is D) -9+9
What is equivalent to the equation y=3x+z/4?
Answers
y=3x+ 1/4z
Area of a rectangle
Equation
Answers
Therefore, equation is A=2(l+b)
A student received a coupon for 12% off the total purchase price at a clothing store. Let b be the
original price of the purchase. Use the expression below for the new price of the purchase. Write an
1. equivalent expression by combining like terms.
b-0.12b
Answers
Answer:
the equivalent expression is 0.88(x)
Step-by-step explanation:
Given that
There is 12% off on the total purchase price
Based on the above information
The expression that used the given terms i.e.
b - 0.12b
i.e.
1 - 0.12
= 0.88(x)
Hence, the equivalent expression is 0.88(x)
Find the circumference and area of the circle. Use 3.14 for π. Round to the nearest hundredth if necessary. r = 2m
Answers
The answer is 12.57
But rounded to the nearest tenth is 12.6
What is the end behavior for the graph of the function
f(x)=9/10 log [-(x + 9)] + 10?
Answers
Answer:If you draw a graph or look it up on Desmos, it curves down around y = 10. It only hits the second and third quadrant. B is the only situation that describes this.
Step-by-step explanation:g
How many 1/6 pound servings are in 10 pounds of chicken ? Pls help
Answers
Answer:
60
Step-by-step explanation:
1/6 * 60 = 60/6
60/6 = 10/1 = 10
The number of 1/6 pound servings in 10 pounds of chicken is; 60
Division of fractionWe are required to determine how many 1/6 pound servings are in 10 pounds of chicken.
Hence ; we have;
10 ÷ 1/610 × 6/1= 60.
Read more on divisions;
https://brainly.com/question/1622425
When dealing with word problems and linear equations, what does the y-intercept represent and how is the slope defined?
a.
y-intercept represents the final value, slope is increasing
c.
y-intercept represents the starting value, slope is the rate of change
b.
y-intercept represents the final value, slope is decreasing
d.
y-intercept represents the starting value, slope is decreasing
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
C
Step-by-step explanation:
y-intercept represents the starting value, slope is the rate of change
slope is rise/run
Answer:
C is correct! :D
Step-by-step explanation:
Edge nuity 2021
Which equation(s) represents a nonproportional relationship? Select all that apply
O y = 3x
O y = 3x-2
O y=x+1
O y=-4x
O y=-2-4
Answers
Don’t click on the other comment, that link is a hack
what is the answer of 17x12
Answers
Answer:
204
Step-by-step explanation:
17x12=204
Exams are approaching and Helen is allocating time to studying for exams. She plays for the very successful women's lacrosse team and must schedule her studying around lacrosse practices and play-off games. She thinks that with the appropriate preparation, she has a 70% chance of getting an A in Marketing. She also believes that this chance will decrease to 60% if the lacrosse team makes the play-offs. Are getting an A on the exam and being in the lacrosse play-offs independent events?
Answers
Answer:
No, there events are dependent, because the change of getting an A in Marketing decreases if the lacrosse team makes the playoffs.
Step-by-step explanation:
Independent events:
Two events are said to be independent if one event happening, or not, does not change the probability of the other event happening.
In this question:
The change of getting an A in Marketing decreases if the lacrosse team makes the playoffs, which implies that the events are dependent, an the answer is no.
pleeeaassseee brainliest to first person
Answers
Answer:
B. 128
Step-by-step explanation:
Answer:
by using Pythagoras law
hypotenuse ²=perpendicular ²+base²
h²=100²+80²
h²=10000+6400
h=√16400=128.06m
128m is the required answer.
Omg!! Please help!! Thank you
Answers
Answer:
the first one since it shows all the lines being equal and therefore making the angles equal
Answer:
AB=DE, BC=EF, AC=DF
Step-by-step explanation:
The first one is correct
Order the angles from smallest to largest, I need help with it
Answers
Answer: <F, <D, <E
Step-by-step explanation:
The smallest angle is determined by looking at the shortest side, and then going across from it. Then medium, 5, across. And so on.
What is the slope of the line that contains these
points?
X=
-1 1
3
5
у=
10
2
-6
-14
Answers
Answer:
The slops is -4
Step-by-step explanation:
Given
x: -1 1 3 5
y: 10 2 -6 -14
Required
The slope
Pick any pair of x and y
[tex](x_1,y_1) = (-1,10)[/tex]
[tex](x_2,y_2) = (1,2)[/tex]
The slope is:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{2 -10}{1 --1}[/tex]
[tex]m = \frac{-8}{2}[/tex]
[tex]m = -4[/tex]
Solve the system of equations.
y = 6x + 13
y = 2x + 1
a.
( 5, 3)
c.
( 3, -5)
b.
( -3, -5)
d.
No solution
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
b.
( -3, -5)
Step-by-step explanation:
6x + 13 = 2x + 1
6x -2x = 1-13
4x = -12
x = -12/4 = -3
y = 6x + 13
y = 6(-3) +13 = -18+13 = -5
(x, y) = (-3,-5)
6x+13=2x+1
6x-2x=1-13
4x= -12
x= -12/4
x= -3
y=6(-3) +13
y= -18+13
y= -5
(x,y)=(-3,-5)
2x+9 = 35 solve for x
Answers
Answer:
x=13
Step-by-step explanation:
2x+9=35
2x=35-9
2x=26
x=26/2
x=13
workout the following divisions:
Answers
Answer:
I think this is the same as yesterday.
Pls help!!!! Thank you
Answers
Answer: No.
Step-by-step explanation: YOU ALREADY HAVE THE ANSWER
6y-5=7 two step equations
Answers
Answer:
The answer is y = 2.
Step-by-step explanation:
1) Add 5 to both sides.
[tex]6y = 7 + 5[/tex]
2) Simplify 7 + 5 to 12.
[tex]6y = 12[/tex]
3) Divide both sides by 6.
[tex]y = \frac{12}{6} [/tex]
4) Simplify 12/6 to 2.
[tex]y = 2[/tex]
Thus, the answer is y = 2.
The value of y in 6y-5=7 is 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
6y-5=7
Now, solving for y
Add 5 both side
6y-5 + 5=7 +5
6y= 12
Now, divide both side by 6
6y/6 = 12/6
y= 2
Hence, the value of y is 2.
Learn more about Equation here:
https://brainly.com/question/10413253
#SPJ2
How can I prepare for the math sat as someone who really struggles to understand math.. videos aren’t really helping
Answers
Answer:
i could tutor you
Step-by-step explanation:
Answer:
Khan Academy. Just do some work on different topics you have learned. Brush up on it. They have practice problems, assessments, and assignments. If you need help they have hints and videos.
I'm terrified of the SAT but i have to take the Pre SAT soon and i haven't been learning anything with online school.
Step-by-step explanation:
Y’all help meeeee :(
Answers
If Siny = x Sin (a+y). Prove that
dy/dx=[Sin²(a+y)]/Sina
Answers
Answer:
Use Trigonometric formulae to simplify expressions
Step-by-step explanation:
Re-order to group the x and y,
Sin(y) / Sin(a+y) = x
to differentiate apply d/dx to both sides
[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x
use division rule on left side which will give
[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1
Group them so dy/dx is on the left hand side:
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)
Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]
Simplify it
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))
La torre de pisa tiene una altura aproximada de 56m. Actualmente, la torre se separa de la vertical una distancia de 3,9m. halla la longitud de la vertical desde la cima de la torre hasta el suelo.
con procedimiento porfavor.
Answers
Answer:
Raíz cuadrada de (3.9)^2+(56)2
Step-by-step
C^2= a^2+b^2
Sabes que la c es la distancia del punto más alto de la Torre hasta donde llega tu vista
Which formula would you enter into D3, and then AutoFill into D4 to D6, to calculate the winning percentage (Pct.) for the teams?
Answers
Formula to calculate percentage are=
Winning match/total match *100
And copy paste formula of VLOOKUP in to desire cell formula bar.
Example in spreadsheet :
Winning match=A5
Total match=A6
Write formula in cell D3:
=(A5/A6)*100
And write formula of VLOOKUP into cell D4-D6 to retrieve data from desire cell.
6-4x is Less than or equal to 26
Answers
A rope 55 feet long is cut into two pieces. If one piece
is 23 feet longer than the other, what is the length, in
feet, of the shorter piece?
A. 2
B. 16
C. 23
D. 32
E. 51
Answers
Answer:
the answer is D
Step-by-step explanation:
55-23=32
Answer:
16
Step-by-step explanation:
shorter piece measures x
longer piece measures x +23
Together they measure 55 ft
x + (x+23) = 55
2x + 23 = 55
-23 = -23
____________________
2x = 32
x = 16