Answers
Answer:
[tex]\displaystyle f'(1) = 6[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = 5x - 1 + \ln x[/tex]
Step 2: Differentiate
[Function] Derivative Property [Addition/Subtraction]: [tex]\displaystyle f'(x) = \frac{d}{dx}[5x] - \frac{d}{dx}[1] + \frac{d}{dx}[\ln x][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle f'(x) = 5 \frac{d}{dx}[x] - \frac{d}{dx}[1] + \frac{d}{dx}[\ln x][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle f'(x) = 5 - 0 + \frac{d}{dx}[\ln x][/tex]Logarithmic Differentiation: [tex]\displaystyle f'(x) = 5 + \frac{1}{x}[/tex]Substitute in x: [tex]\displaystyle f'(1) = 5 + \frac{1}{1}[/tex]Simplify: [tex]\displaystyle f'(1) = 6[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Related Questions
Which of the following statements would not translate to the equation 8 ÷ x = -4?
A. Eight divided by a number is equal to negative four.
B. The solution of a number divided by eight is negative four.
C. The quotient of eight and a number equals negative four.
D. If eight is divided by a number, the result is negative four.
Answers
Answer:
B
Step-by-step explanation:
B it's wrong because 8 is divided by a number not a number by 8
3x^2 + 2x^2=
6x^3 - 2x^3=
first answer gets brainiest :)
Answers
Answer:
1) [tex]13x^{2}[/tex]
2) [tex]208x^{6}[/tex]
Step-by-step explanation:
(3*3(x)^2) + (2*2(x)^2) = 9x^2 + 4x^2 = 13x^2
(6*6*6(x)^3) - (2*2*2(x)^3) = 216x^3 - 8x^3 = 208x^3
How much larger is 10 7 than 10 3 What operation can we use?
Answers
Answer:
9,999,000
subtraction
Step-by-step explanation:
We can compare numbers using subtraction or division.
A question like "how much larger" usually means a comparison by subtraction. For example, how much larger is 10 than 8. Use subtraction: 10 - 8 = 2. Answer: 2.
A question like "how many times larger" usually means a comparison by division. For example, how many times larger is 30 than 5? Use division: 30/5 = 6. Answer: 6.
Here, the question is "how much larger" not "how many times larger," so we will compare with subtraction.
10^7 - 10^3 = 10,000,000 - 1,000 = 9,999,000
Two functions are given.
f(x)=-x^2+3x-2
g(x)=-x+1
What is one value for x such that f(x)=g(x)?
Answers
Hi
f(x) = g(x) if -x²+3x-2 - ( -x+1) = 0
-x² +3x-2 +x-1 = 0
-x² +4x -3 = 0
To solve, tou have to use the general method of resolution of a quadratic fonction.
To determine if it's has a solution in R, let's calculate Δ
Δ = (4)² - 4 * (1) *(-3)
Δ = 16 +12
Δ= 28
as Δ≥ 0 so the function allow two solution within R
so S 1 = ( -4 +√28) / 2 S 2 = (-4 -√28 ) /2
S1 = ( -4 + 2√7) /2 S2 = (-4 - 2√7) /2
S1 = (2 (-2 +√7) /2 S2 2 (-2 -√7) /2
S1 = -2 +√7 S2 = -2 -√7
So the two function are equal twice. one for x = -2 +√7 and second x = -2-√7
question below :) i suck at math
Answers
Step-by-step explanation:
You plug g(3) into the equation like this
g(3) = -x - 2
what is positive 1 plus negative 6
Answers
Answer:
-5
Step-by-step explanation:
When answering these problems, I like to think of dirt stacks. (Weird, but it helps.)
Okay, so you have a stack of dirt one foot off the ground. Then you dig six feet down, including the stack. Because the stack will be 5 feet into the ground now, the answer is -5.
The reflection of point S across the y-axis is point
. The reflection of point Q across the x-axis and the y-axis is point
, whose coordinates are (
,
).
Answers
Also point V
(-5,-5.5)
I'LL GIVE BRAINLIST!! THERES 2 ANSWERS!! PLEASE HELP!!
Answers
Answer:
i would go with option 2, just depending on how many pounds u get for $6.58 though.
A farmer sells his com for $320 a metric ton with a small surcharge of $25. His neighbor sells her corn crop for $320 a
metric ton and gives a $20 rebate. Write the cost model equations for both farmers and find the amount of corn that
makes the costs equal.
Answers
Please help
29.25 + (−47.5)
Answers
Answer: -18.25 is your answer.
because there is one negative sign so you know your answer negative. So 29.25 + -47.6 = -18.25
Step-by-step explanation:
8x+3y=14,2x+y=4. PLz solve this it’s emergency
Answers
Answer:
x=1, y=2
Step-by-step explanation:
1) 8x+3y=14 Original system of linear 2d equations
2x+y=4
2) 8x+3y=14
-4 (2x+y) =-4(4) Multiply second equation by negative four.
3) 8x+3y=14
+ -8x-4y=-16 Add equations, eliminating x terms
4) -y=-2
y=2 solve for y
5) 8x+3(2)=14 Substitute solution for y to solve for x
8x=14-6
8x=8
x=1
Simple Inequalities:
2 <6
29
Which compound inequality and graph match the given simple inequalities?
Answers
I think it is the first option. hope this helps :)
Tyler gathered data from 12 recent basketball games about the number of points he scored, the number of points his teammate Nolan scored, and the total number of points his team scored. He displayed the data in two scatter plots.
Does either scatter plot indicate a positive correlation between the variables?
Answers
Answer:
Only plot B
Step-by-step explanation:
Answer:
Only Plot B
Step-by-step explanation:
The points in plot A are randomly scattered, and there is no recognizable pattern. So, this plot indicates no correlation between the points Tyler scored and the points Nolan scored.
In plot B, the total points Tyler’s team scored appear to increase as the points Tyler scored increase. This pattern indicates a positive correlation between the two variables.
So, only plot B indicates a positive correlation.
Ludmilla Pavel is paid a commission on all sales over $3,000 a week. Last week she earned a commission
of $420 on sales of $16,000. What rate of commission was she paid to the nearest tenth percent
Answers
Answer:
Since she sold $16,000, she earned commission on $13,000 of it.
So she earned $420 from $13,000
420/13000 = 0.0323 which is 3.23% or 3.2% to the nearest tenth %
10
Step-by-step explanation:
Answer:
3.23% or 3.2% to the nearest tenth %
Step-by-step explanation:
Since she sold $16,000, she earned commission on $13,000 of it. So she earned $420 from $13,000. 420/13000 = 0.0323 which is 3.23% or 3.2% to the nearest tenth %
Hey friends! If u guys wanna help I’d really appreciate it! I’m in need of some help rn lol I’ll give u all my points!!!!!
Answers
Answer: it’s C
Step-by-step explanation:
Karla needs 3.7 pounds of chicken. If each pound of chicken costs $4.50, how much will she need to spend altogether?
Answers
Answer: $16.65
Step-by-step explanation:3.7*$4.50=$16.65
5200 at 4% for 3 years ??
Answers
= 5849.3
Pls help! What is mSN ?
Answers
Answer:
ur ugly face
Step-by-step explanation:
ooooooooooooooooooooooooooooooo
A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 on a taxi ride. How many miles can Andrea travel? Select all that apply. PLEASE HELP!!
A. 18
B. 16
C. 14
D. 12
E. 10
Answers
Answer:
losien yo hablo español espero que alguien mas te ayude
Answer:
Your answer would be C , D, E
Step-by-step explanation
Have a Great day!
Select the graph of g(x) = |-2х + 6|
can someone tell me if this is right
Answers
Answer:
no
Step-by-step explanation:
the graph should be facing up.
Suppose 15% of x equals 20% of y. What percentage of x is y?
a) 5 b) 35 c) 75 d) 133 1/5 e) 300
Answers
Answer:
c)15
Step-by-step explanation:
Confirmed by rsm
A percentage is a way to describe a part of a whole. x is 133¹/₃% of y. The correct option is D.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that 15% of x equals 20% of y. Therefore, we can write,
15% of x = 20% of y
(15/100) × x = (20/100) × y
Multiply both the sides of the equation by 100,
(15/100) × x × 100 = (20/100) × y × 100
15x = 20y
x/y = 20/15
Divide both the sides of the equation by 5,
x/y = 4/3
Now, the percentage of x that is y is,
Percentage = (x/y) × 100%
= (x/y) × 100%
= (4/3) × 100%
= 133.33%
= 133 ¹/₃ %
Hence, x is 133.33¹/₃% of y.
Learn more about Percentages here:
https://brainly.com/question/6972121
#SPJ2
EASY QUESTION HELP AND HURRRYYYYY!!!!
Answers
Answer:
d
Step-by-step explanation:
Answer:
D, s=v
Step-by-step explanation:
although its scaled, the angles are equal to each other. pls brainliest im new and never got brainliest before thx appreciate it
Part 1: Given triangle ABC and AC = BC, find a and the side lengths of the triangle. C 6a - 8 4a-2 MathBits.com A B Side BC = Side AC = Part 2: Based off your knowledge of side lengths and triangles, what can you for sure classify the above triangle as Triangle ABC:
Answers
Answer: a = 2; AC = BC = 10
Step-by-step explanation:
AC = BC => 6a - 8 = 4a - 2
<=> 2a = 6
<=> a = 3
=> AC = 6.3 - 8 = 10
AC = BC => BC = 10
Anyone? Would appreciate it.
Answers
Answer:
correct
Step-by-step explanation:
the function 56-4y=-5x can be used to determine the total amount of money in a coin jar,y,after money is added for x days. what is the rate of change in dollars with respect to the number of days?
Answers
Answer:
23
Step-by-step explanation:
An ice cream shop is testing some new flavors of ice cream. They invent 25 new flavors for customers to try, and throw out the 13 least popular flavors. The shop makes 80 cartons of each of the remaining flavors. It takes 2 cartons to get one liter(L) of ice cream How much total ice cream is in the cartons?
Answers
Answer:
960 cartons
Step-by-step explanation:
Ice cream shop invented 25 new flavors of the ice cream out of which 13 flavors were discarded by the ice cream shop as they were least popular.
So flavors left = 25 - 13 = 12
The shop made 80 cartons each of 12 flavors so total number of cartons = 12×80 = 960 cartons
Therefore answer will be 960 cartons of remaining flavors
plz mark brainly
Please finish 13,14,15 please I will give 10 points and brainliest
Answers
13. 2.5
14. -2
15. 1.5
Equations:
13. y=2.5x-3
14. y=-2x+1
15. y=1.5x-8
You have piano lessons every fourth day and guitar lessons
every sixth day. Today you have both lessons. In how many days will
you have both lessons on the same day again? Show your work.
Answers
All I did was multiply both the 4 and the 6 which gave me 24.
please help me please please nice brainly people pls
Answers
Answer:
I think your answer is B= 12.
Step-by-step explanation:
Its x times 1 .33333 = y
brainliest?
The next section (This is the last five, don't worry xd)
7th grade math
I will give brainliest!
2 = a/6
find the value of a
Answers
Answer:
a = 12
Step-by-step explanation:
Given
2 = [tex]\frac{a}{6}[/tex] ( multiply both sides by 6 to clear the fraction )
12 = a
Answer:
a = 12
Step-by-step explanation:
We can do the inverse of division which is multiplication. 6 x 2 equals 12 and if we substitute 12 for a (12 divided by 6) you get 2 hope that helpss!!!