Let f(x) = x^6( x − 8 )^7 / (x^2 +2)^2
Use logarithmic differentiation to determine the derivative.
f ' (x) =________
If
f(x) = x⁶ (x - 8)⁷ / (x² + 2)²
then taking the logarithm of both sides lets us expand the right side as
ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)
ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)
using the property ln(ab) = ln(a) + ln(b).
We can also use the property ln(aⁿ) = n ln(a), so that
ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)
Then differentiating both sides using the chain rule gives
f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)
f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)
f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)
Solve for f'(x) :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)
and replace f(x) with the given function :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²
We can expand the product :
f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³
then simplify by factoring :
f'(x) = x⁵ (x - 8)⁶/(x² + 2)³ • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))
Simplify the rest :
f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³
The perimeter of a rectangle is 20/33 feet. The length of three sides together is 16/33 feet.
What is the length of the fourth side?
40 feet
4/33feet
16/33feet
20/33feet
Answer:
40 feet
Step-by-step explanation:
on edge
you buy 2.3 pounds of apples for $1.43 per pound. how much do you spend
Answer:
$3.36
Step-by-step explanation:
$1.43 = 1 lbs
$1.43 + $1.43 = $2.86
$2.86 + .3 = $3.36
the elevation of the salton sea in california is 66 meters below sea level. which integer best represents this elevaton in meters?
please help
Answer:
-66
Step-by-step explanation:
If we use 0 as the centre of all numbers, and another number is 66 below this baseline, we could say that it is -66 meters above sea level, or 66 meters below sea level.
select the correct product for the problem below. (−85)(23)(−4) =? -64/15 64/15 16/60 -16-60 64-60
Answer: 7,820
Sorry I have no help :(
On Monday there are 25 pencils in a basket, If 3 pencils are taken out of the basket each day, how many pencils are left in the basket on Friday?
13 cuz add 4 days then friday so 4×3 which is 12 and 12-25 so ye its 13
The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes.
a. What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?
b. Without assuming anything about the distribution of times, at least what percentage of the times is between 25 and 45 minutes?
c. Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 20 minutes or greater than 50 minutes?
d. Assuming that the distribution of times is approximately normal, about what percentage of times are between 25 and 45 minutes? less than 20 minutes or greater than 50 minutes? less than 20 minutes?
68% are within 30 minutes to 40 minutes, 95% are within 25 minutes to 45 minutes and 99.7% are within 20 minutes to 50 minutes
The three sigma rule states that 68% are within one standard deviation of the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.
Given that μ = 35, σ = 5
68% are within one standard deviation = μ ± σ = 35 ± 5 = (30, 40)
95% are within two standard deviation = μ ± 2σ = 35 ± 2*5 = (25, 45)
99.7% are within three standard deviation = μ ± 3σ = 35 ± 3*5 = (20, 50)
`Find out more on three sigma rule at: https://brainly.com/question/25966249
after a party 3/4 cake is leftover. Dennis eats 1/2 of the leftover cake. Which fraction model represents the amount of cake Dennis eats?
in hillary's garden, she has 5 variety of snake plants and 15 variety of orchids. what is the ratio of snake plants to orchids?
Answer:
1:3
Step-by-step explanation:
She has 1 snake plant for every 3 orchids.
You use a garden hose to fill a wading pool. If the water level rises 16 centimeters every 7 minutes
and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change at which the water level rises is ____ centimeters per minute. So solving the equation ____ for y gives a y-value equal to ____
What is 196.7 16 in simplest form?
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 < x < 7.
f(x)
3
5
4.
9
5
15
6
23
7
33
Answer:
Submit Answer
attempt 2 out of 2
Answer:
8
Step-by-step explanation:
It appears your table includes points (4, 9) and (7, 33). The average rate of change on the interval is the slope of the line between these two points:
m = (y2 -y1)/(x2 -x1)
m = (33 -9)/(7 -4) = 24/3 = 8
The average rate of change is 8.
The local movie theater, Scene It Cinema, had a special showing of the latest dinosaur movie. There were 6 youth tickets sold for every 5 adult tickets sold.
If there were 70 adult tickets sold, how many movie tickets were sold altogether?
Answer:
Let the youth and adult tickets be y and x respectively.
6y + 5x ---> (1)
From statement (1):
(1) × 14
84y + 70x
For every 70 adult tickets sold, 84 youth tickets were sold.
Total number of tickets sold= 70 + 84
= 154
you have to solve for X
Answer:
x = 5/8Step-by-step explanation:
(1/2) / 4 = x / 51 / 8 = x / 5x = 5 / 8Done
Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 924 square milimetres and its perimeter is 122 milimetres.
Length =l
Height = h
Area function = l * h = 924
Perimeter function = 2i + 2h = 122
Divide by 2
I + h = 61.
Plug in I or h for the other variable
I * (61 - I) = 924
61i - i^2 = 924
Factor the function
(-I + 28)(I - 33) = 0
l = 33 as l cannot be negative
61 - 33 = 28
h = 28
Difference between h and l is 33-28=5
5(x-a)=3(x+b)
Solve for x
Answer:
[tex]x=\frac{3b}{2} +\frac{5a}{2}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
5(x - a) = 3(x + b)
5x - 5a = 3x + 3b
2x = 5a + 3b
x = 2.5a + 1.5b
Answer this by 4:20 EST and I will mark brainliest
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, a ) and (x₂, y₂ ) = (9, - 4 )
m = [tex]\frac{-4-a}{9-6}[/tex] = [tex]\frac{-4-a}{3}[/tex]
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
2x - 3y = 6 ( subtract 2x from both sides )
- 3y = - 2x + 6 ( divide through by - 3 )
y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes , then
[tex]\frac{-4-a}{3}[/tex] = [tex]\frac{2}{3}[/tex] , so
- 4 - a = 2 ( add 4 to both sides )
-a = 6 ( multiply both sides by - 1 )
a = - 6 → A
Which one has more kinetic energy water or boiling water
Answer: 5
Step-by-step explanation:
because idek sorry
how long did it take for Car A to travel 10 meters
Answer:
isnt it 5 seconds?
its quite blurry but i think its 5
It took car A five seconds to travel 10 meters. The 5 on the x-axis aligns with the 10 meters on the y-axis.
Which statements are correct interpretations of this graph?
Select each correct answer.
a.4 boxes are filled every 3 min.
b.3 boxes are filled every 4 min.
c.1.3 boxes are filled per minute.
d.0.75 boxes are filled per minute.
x - y = 3
b) Work out the value of 2x – 2y
How would the expression x3 -3 sqrt 3 be rewritten using difference of cubes?
O A. (x- 13 )(x2-3x - 3)
O B. (x+ 3)(x + 13 x + 3)
C. (x - 13 )(x2 + 3x + 3)
O D. (x- vb)(x2 + v3 x+3)
Answer:
x^3 - (√3)^3
I'm not so sure since it's not even an option
Step-by-step explanation:
x^3 - 3√3 = x^3 - 3^1 × 3^(1/2)from the laws of indices: 3^1 × 3^(1/2) = 3^(1 + 1/2)= 3^(3/2) which is the same as (√3)^3so it could be written as x^3 - (√3)^3please help will brain list if correct no links please
Answer:
C
Step-by-step explanation:
the angle opposite of it is 30
Does (–1, 2) make the equation y = x + 9 true?
Answer:
(-1, 2) does not make the equation y=x+9 true.
Step-by-step explanation:
y=x+9
(-1, 2)=(x, y)
2=(-1)+9,
-1+9=8,
2 does not equal to 8.
Answer: No.
PLZ SOLVE THE PROBLEM
Answer:
[tex]-2\frac{1}{2}[/tex]
Step-by-step explanation:
→ Minus the 2 numbers from each other
[tex]-1\frac{1}{5} -1\frac{3}{10}[/tex]
→ Find the LCM
[tex]-1\frac{2}{10} -1\frac{3}{10}[/tex]
→ Simplify
[tex]-2\frac{5}{10} =-2\frac{1}{2}[/tex]
Find an expression with represents the sum of 5X -8 and 2X +2 in simplest terms
13*10-20 im in a hurry
Answer: 110
Step-by-step explanation:
13*10 = 130-20 is 110
The answer: 13 × 10 - 20 = 130 - 20 = 110
OK done. Thank to me :>
Christina has 6 pieces of candy in her lunchbox. Rachel gives Christina more pieces of candy. Now Christina has 18 pieces of candy. How many pieces of candy did Rachel give Christina?
18 - 6 = 12
When subtracting the new amount by the original amount, you will find the change or the amount that Rachel gave
18 - 6 = 12
So, Rachel gave Christina 12 pieces of candy.
Answer:
18-6=12
She gave her 12 more pieces of candy.
hope this helps.
this is long division… please help
Answer:
23.35
Step-by-step explanation:
When a guy says i cheated just to let the world know what does it mean?
Answer ASAP
Answer:
He says that because he thinks ur cheating for attention. When they say you 'let the whole world know' that you`re unloyal and can be with any guy, without a care, it`s an insult.
Answer:
it means that he was dating another person while already dating
Step-by-step explanation:
it like when ur dating 2 people at one time without the other person knowing