f(x,y)=x10-3xy2then fz=
A. 10 x9 - 3y2
B. 20 x9 - 3y2
C. 2y2
D. 10x10 + xy2
which option is correct please
Answers
Given:
The function is:
[tex]f(x,y)=x^{10}-3xy^2[/tex]
To find:
The value of [tex]f_x[/tex].
Solution:
We need to find the value of [tex]f_x[/tex]. So, we have to find the first order partial derivative of the given function with respect to x.
We have,
[tex]f(x,y)=x^{10}-3xy^2[/tex]
Differentiate partially with respect to x.
[tex]f(x,y)=\dfrac{\partial}{\partial x}x^{10}-3y^2\dfrac{\partial}{\partial x}x[/tex]
[tex]f_x=10x^{10-1}-3y^2(1)[/tex]
[tex]f_x=10x^{9}-3y^2[/tex]
Therefore, the correct option is A.
Related Questions
Find the first, second, third and fourth order Maclaurin polynomials of f(x) =
arctan(x). Draw the graph of f(x) and the four polynomials on the same
diagram. (Sketch by hand or use software.)
#urgent please give me this answer and help me#
Answers
The first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:
The first order Maclaurin polynomial is f(x)=xThe second order Maclaurin polynomial is also f(x)=xThe third order Maclaurin polynomial is [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]The fourth order Maclaurin polynomial is also [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]You can see the graph on the attached picture.So let's start by finding the first order maclaurin polynomial:
f(x)=f(0)+f'(0)x
so let's find each part of the function:
f(0)=arctan(0)
f(0)=0
now, let's find the first derivative of f(x)
f(x)=arctan(x)
This is a usual derivative so there is a rule we can use here:
[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]
so now we can find f'(0)
[tex]f'(0)=\frac{1}{(0)^{2}+1}[/tex]
f'(0)=1
So we can now complete the first order Maclaurin Polynomial:
f(x)=0+1x
which simplifies to:
f(x)=x
Now let's find the second order polynomial, for which we will need to get the second derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}[/tex]
so:
[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]
we can rewrite this derivative as:
[tex]f'(x)=(x^{2}+1)^{-1}[/tex]
and use the chain rule to get:
[tex]f''(x)=-1(x^{2}+1)^{-2}(2x)[/tex]
which simplifies to:
[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]
now, we can find f''(0):
[tex]f''(0)=-\frac{2(0)}{((0)^{2}+1)^{2}}[/tex]
which yields:
f''(0)=0
so now we can complete the second order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}[/tex]
which simplifies to:
f(x)=x
Now let's find the third order polynomial, for which we will need to get the third derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}[/tex]
so:
[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]
In this case we can use the quotient rule to solve this:
Quotient rule: Whenever you have a function in the form , then it's derivative is:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
in this case:
p=2x
p'=2
[tex]q=(x^{2}+1)^{2}[/tex]
[tex]q'=2(x^{2}+1)(2x)[/tex]
[tex]q'=4x(x^{2}+1)[/tex]
So when using the quotient rule we get:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
[tex]f'''(x)=\frac{(2)(x^{2}+1)^{2}-(2x)(4x)(x^{2}+1)}{((x^{2}+1)^{2})^{2}}[/tex]
which simplifies to:
[tex]f'''(x)=\frac{-2x^{2}-2+8x^{2}}{(x^{2}+1)^{3}}[/tex]
[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]
now, we can find f'''(0):
[tex]f'''(0)=\frac{6(0)^{2}-2}{((0)^{2}+1)^{3}}[/tex]
which yields:
f'''(0)=-2
so now we can complete the third order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}[/tex]
which simplifies to:
[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]
Now let's find the fourth order polynomial, for which we will need to get the fourth derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}+\frac{f^{(4)}(0)}{4!}x^{4}[/tex]
so:
[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]
In this case we can use the quotient rule to solve this:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
in this case:
[tex]p=6x^{2}-2[/tex]
p'=12x
[tex]q=(x^{2}+1)^{3}[/tex]
[tex]q'=3(x^{2}+1)^{2}(2x)[/tex]
[tex]q'=6x(x^{2}+1)^{2}[/tex]
So when using the quotient rule we get:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
[tex]f^{4}(x)=\frac{(12x)(x^{2}+1)^{3}-(6x^{2}-2)(6x)(x^{2}+1)^{2}}{((x^{2}+1)^{3})^{2}}[/tex]
which simplifies to:
[tex]f^{4}(x)=\frac{12x^{3}+12x-6x^{3}+12x}{(x^{2}+1)^{4}}[/tex]
[tex]f^{4}(x)=\frac{6x^{3}+24x}{(x^{2}+1)^{4}}[/tex]
now, we can find f^{4}(0):
[tex]f^{4}(x)=\frac{6(0)^{3}+24(0)}{((0)^{2}+1)^{4}}[/tex]
which yields:
[tex]f^{4}(0)=0[/tex]
so now we can complete the fourth order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}+\frac{0}{4!}x^{4}[/tex]
which simplifies to:
[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]
you can find the graph of the four polynomials in the attached picture.
So the first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:
The first order Maclaurin polynomial is f(x)=xThe second order Maclaurin polynomial is also f(x)=xThe third order Maclaurin polynomial is [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]The fourth order Maclaurin polynomial is also [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]You can find further information on the following link:
https://brainly.com/question/17440012?referrer=searchResults
I need help completing this answer are you available
Answers
Answer:
Step-by-step explanation:
Four seconds pass between the first and third flash of a strobe light. The rate at which the strobe flashes is constant. How many seconds will pass between the first and the twelfth flash of the same light?
Answers
Answer:
t = 22 s
Step-by-step explanation:
If n is the number of strobe pulses
The first strobe pulse occurs at t = 0
t = 2(n - 1)
t = 2(12 - 1)
t = 2(11)
t = 22 s
I need help ASAP thank you
Answers
9514 1404 393
Answer:
C
Step-by-step explanation:
The graph shows two vertical asymptotes, so the relevant function will be zero in the denominator for two different x-values. The only possibility is ...
[tex]F(x)=\dfrac{1}{(x-1)(x+1)}[/tex]
Question 2 of 10
Which pair of functions are inverses of each other?
O A. f(x) = i +15 and g(x) = 12x - 15
O B. f(x) = - 10 and g(x) = 2410
O C. f(x) = y3x and g(x) = (3) 3
O D. f(x) = 11x- 4 and g(x) = 4
SUBMIT
Answers
Answer:
option c f(x)=-10and g(x)=2410
The minimum point of the graph y = 2x^2 + 2x +1 is located at:
Answers
Answer:
A
Step-by-step explanation:
By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)
Find the solutions of the quadratic equation x2 + 7x + 10 = 0.
Question 13 options:
A)
x = 2, 5
B)
x = –2, –5
C)
x = –7, –3
D)
x = 7, 3
Answers
Answer:
Step-by-step explanation:
x² + 7x + 10 = 0
x = [-7 ± √(7² - 4·1·10)]/(2·1) = [-7 ± √9[/2 = [-7 ± 3]/2 = -2, -5
Find the area of the circle. Use 3.14 for tt. d = 6 ft A = [?] ft2 A=Tr2
Answers
d=6ft
According to formula A=πr²
first we need 'r'
Hence,
as, r=d/2
r=6ft/2
r=3ft
A=πr²
A=3.14(3ft)²
A=3.14×9ft²
A=28.26ft²
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
Answers
Answer:
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
PLEASE HELP!!! ITS DUE TONIGHT!!!!!
YOUR ASSIGNMENT: Difference of 10
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game.
Your Player
1. Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer)
a. Which player did you select?
b. What number did the other player pick?
Modeling Ways to Win
2. Should you use an equation or an inequality to represent the ways your player can win? Why? (2 points: 1 point for an answer, 1 point for an explanation)
3. Imagine that Erik chose a 4 and Nita chose a 12. Would the winner be different if Nita chose the 4 and Erik chose the 12? (2 points: 1 point for an answer, 1 point for an explanation)
4. Is it appropriate to use an absolute value inequality to represent how a player wins this game? Why? (2 points: 1 point for an answer, 1 point for an explanation)
5. If your player is Erik, write an inequality that shows all of the ways that Erik will win if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways that Nita will win if Erik chooses 17.
Be sure to define your variable. (3 points: 1 point for defining the variable, 2 points for the correct inequality)
6. In order to graph your solutions, solve for the variable. Be sure to show your work. (2 points)
7. Sketch a graph of your solutions. (2 points: 1 point for endpoints, 1 point for the correct region)
Forming a Strategy and a New Rule
8. What is the range of numbers that will win the game for your player?
If your player is Erik, assume that Nita chooses 7.
If your player is Nita, assume that Erik chooses 17.
(Hint: Remember that Erik and Nita can choose only numbers from 0 to 20, inclusive.) (2 points)
9. Graph all the possible numbers that either player could pick. Compare this graph with your answer in question 8.
If your player is Erik, and Nita chooses 7, does Erik have a good chance of winning?
If your player is Nita, and Erik chooses 17, does Nita have a good chance of winning?
Explain your answer. (3 points: 1 point for the correct graph, 2 points for the explanation)
Answers
Answer:
it is too long send me link of it
Answer: Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer) a. Which player did you select? Erik, assume that Nita chooses 7. b. What number did the other player pick? 17
2. Should you use an equation or an inequality to represent the ways your player can
win? Why? (2 points: 1 point for an answer, 1 point for an explanation)
An algebraic statement that represents all the ways Eric will wins is
where
be the number that Eric thi
3. Imagine that Erik chose a 4 and Nita chose a 12. Would the winner be different if
Nita chose the 4 and Erik chose the 12? (2 points: 1 point for an answer, 1 point for
an explanation)
no because both nita and eric won. eric with a number less than than 10
and nita with a number more than 10.
4. Is it appropriate to use an absolute value inequality to represent how a player wins
this game? Why? (2 points: 1 point for an answer, 1 point for an explanation)
they win it remains positive the negative will be losses which will be changed due to
absolute value
5. If your player is Erik, write an inequality that shows all of the ways that Erik will win
if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways
that Nita will win if Erik chooses 17.
Be sure to define your variable. (3 points: 1 point for defining the variable, 2 points for
the correct inequality)
Step-by-step explanation:
A few more problems and then I’m done
Answers
Answer:
((c)).g(x) = 3 × 2^x +2..
If you have 2 distinct black playing cards and 2 distinct red playing cards, how many ways can you arrange the four cards given that the red cards can never be next to each other
Answers
Answer:
I'm not 100% on the interoperation of this question...
are the two red cars out of a 52 card deck and you can try all the combinations of two red and black cards ????
for this answer i will assume that you have 4 coins two nickels and 2 quarters
and the question is " how many ways can you arrange the four coins given that the nickels can not be next to the quarters"
in that case I think the answer is 8
Step-by-step explanation:
1- N1 Q1 N2 Q2
2- N1 Q2 N2 Q1
3- N2 Q1 N1 Q2
4- N2 Q2 N1 Q1
5- Q1 N2 Q2 N1
6- Q2 N2 Q1 N1
7- Q1 N1 Q2 N2
8- Q2 N1 Q1 N2
[tex]2\cdot \left(\left(2\:choose\:1\right)\:\cdot \:\left(2\:choose\:1\right)\right)[/tex]
Write C=5/9(F-32) in standard form
Answers
Answer:
f360 is the ans
Step-by-step explanation:
Solve the following equation for the given variable
-14 + 6y = -6y + 10
Round your answers to the nearest tenths place.
Help please
Answers
Answer:
y = 2
Step-by-step explanation:
I do not know how to explain how I got the answer
Answer:
y = 2
Step-by-step explanation:
- 14 + 6y = - 6y + 10
-14 - 10 = -6y - 6y collect the like terms
- 24/ -12 = - 12y/ - 12
2 = y
I hope this answers your question
What is the slope of the line that passes through the points (10,8) and (-15,18)?
Write your answer in simplest form.
Answers
Answer:
I believe it is 2/5 fraction
Answer:
-2/5
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 18-8)/(-15-10)
= 10/-25
= -2/5
A small boat can travel at 28 per hour how many hours will it take to go across the bay that is 56 miles wide
Answers
Answer:
2 hours
Remember that time = distance/rate
The distance you need to cover is 56 miles, while you go 28 miles per hour. Using these, we get this:
time=56/28
time=2
So it will take two hours to go across a 56 mile wide bay at 28 mph.
Step-by-step explanation:
Find median of given data : 6,6,7,8,11,19,6
Answers
Answer:
Median =7
Mean = 9
Mode = 6
Step-by-step explanation:
Have a gr8 day!
Answer:
the median is 7
Step-by-step explanation:
6,6,6,7,8,11,19
7 is the middle number
what is the area of the trapezoid?
Answers
Answer:
A = 70 mm²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 10, b₁ = 10, b₂ = 4 , then
A = [tex]\frac{1}{2}[/tex] × 10 × (10 + 4) = 5 × 14 = 70 mm²
One year, Alex bought an antique car for his birthday. During the first year he owned it, the
value of the car gained 10%. During the second year, the value of the car gained another
15% from the previous year. If the value of the car is now $37,950.00, how much did Alex
originally pay for his car?
Answers
Answer:
28462.5
Step-by-step explanation:
During the first year it gained 10% and during his second year he gained 15% so you first add those and you get 25%.
Then you multiply 25% with 37,950.
25/100 * 37950 = 948,750/100
= 9487.5
To get the original amount you subtract 9487.5 from 37,950
37,950 - 9487.5 = 28462.5
So the original amount was 28462.5
Which equation represents a line with slope į and y-intercept -6?
2x +3y=-6
3x - 2y= 6
2x - 3y= 18
3x - 2y= 12
Answers
Answer:
Answer:y=-2/9+3
Step-by-step explanation:
Complete the function table.
Answers
Answer:
B
Step-by-step explanation:
The function given is f(n) = n-3. Plug in n=0 and you will get an output - 3. Plug in n=2 and you will get an output - 1. Hence table B is the answer .
What is the common difference for this arithmetic sequence?
-6,-1,4,9,14,...
A. 6
B. 4
C. 5
D. 3
SUBMIT
Answers
Answer:
5 is the answer to your question
Step-by-step explanation:
the numbers are increasing by +5
Find the area of the figure.
A =
Is it m, m2, or m3
Answers
Answer:
348 m^2
Step-by-step explanation:
The figure is made up of a rectangle 24 m by 12 m, and a triangle with a 24 m base and a 5 m height.
A = LW + bh/2
A = 24 m * 12 m + (24 m)(5 m)/2
A = 288 m^2 + 60 m^2
A = 348 m^2
There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y ratio is 3:1. What is a possible coordinate?
Answers
Answer:
Step-by-step explanation:
Suppose the radius is 1. The parametric equations for the circle are
x = cosθ
y = sinθ
x:y = 3:1
tanθ = ⅓
cosθ = 3/√(1²+3²) = 3/√10
sinθ = 1/√10
The solutions are (3/√10, 1/√10) and (-3/√10, -1/√10).
From the picture, two cylindrical glasses of the same capacity. Find the diameter length (X) of a small glass of water.
8
12
14
10
Answers
Answer:
12
Step-by-step explanation:
πr²h=πr²h
π(4.5)²*10=π(x/2)²4.9
What is the slope of a line that is perpendicular to the line whose equation is ax+by=c?
A. c/b
B. b/a
C. −b/a
D. a/b
Answers
Answer:
b/a
Step-by-step explanation:
ax+by=c
To find the slope solve for y
by = -ax+c
Divide by b
y = -a/b x + c/b
The slope intercept form is y = mx+b where m is the slope
The slope is -a/b
A perpendicular line has a slope that is the negative reciprocal
-1/ (-a/b)
-1 * -b/a
b/a
Pls helppppp,,,,,.....
Answers
Answer:
yall do school right now???and i forgot how to do these sorry
Answer:
18 = 2x-14
or, 2x =18+14
or, 2x =32
or, x=32/2
x=16
2(6x-7)=10
or, 12x-14=10
or, 12x=10+14
or, x=24/12
x=2
I need help answering this question asap
Answers
Answer:
Step-by-step explanation:
Geometry please help me need help I don’t know how to do it
Answers
Answer:
A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)
A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)
Step-by-step explanation:
first everything is shifted down 8 units (x,y-8), so we get A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)
then you multiply by -1 A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)
The sum of a number x and
eleven
Answers
Answer:
what is the sum.
Step-by-step explanation:
Take the sum - 11 =x
