Find the differential of the function. v = 2y cos(xy)

Answers

Answer 1

Given a function f(x,y), the differential of f is given by
[tex]df = f_x dx + f_y dy[/tex]
where [tex]f_x[/tex] is the derivative of f(x,y) with respect to x, while [tex]f_y[/tex] is the derivative of f(x,y) with respect to y.

The function of our problem is[tex]f(x,y)=2y \cos(xy)[/tex]
The derivative in x is
[tex]f_x = 2y(-y \sin (xy))=-2y^2 \sin (xy)[/tex]
The derivative in y is
[tex]f_y = 2 \cos (xy) + 2y (-x \sin (xy))=2 \cos (xy) - 2xy \sin (xy)[/tex]

So, the differential of f(x,y) is
[tex]df= -2y^2 \sin (xy) dx + (2 \cos (xy) - 2xy \sin (xy))dy[/tex]

Answer 2

The differential of the function v = 2y cos(xy) is found using the product rule and the chain rule, yielding dv = 2 cos(xy) dy - 2y sin(xy) (xdy + ydx), which accounts for changes with respect to both x and y.

To find the differential of the function v = 2y cos(xy), we'll need to apply the product rule and the chain rule. The product rule states that the differential of a product of two functions is d(uv) = u dv + v du. The chain rule is used when differentiating composite functions, and it implies that d/dx (f(g(x))) = f'(g(x)) * g'(x).

Applying the product rule, we get:

dv = cos(xy) * d(2y) + 2y *d(cos(xy)).The differential d(2y) is simply 2 dy.For d(cos(xy)), we use the chain rule and get -sin(xy) * d(xy), which further expands to -sin(xy) * (xdy + ydx) by applying the product rule again.

Combining these, the differential dv becomes:

dv = 2 cos(xy) dy - 2y sin(xy) (xdy + ydx).

This equation represents the total differential of the function v with respect to both x and y.

For implicit differentiation examples like in equation In(xy) = x2y3 or systems of differential equations, understanding and applying the product rule, chain rule, and implicit differentiation are essential to calculate derivatives and solve the equations.

Related Questions

Decide whether the sequence is arithmetic geometric or neither 5,-10,20, -40

Answers

Try this option^
note, that all members of this sequence have '-' and '+' and 5*(-2)=-10, -10*(-2)=20; 20*(-2)=-40.
It means, that the suggested sequence is geometric, where b₁=5, q=-2.

A carton has a length of fraction 2 and 2 over 3 feet, width of fraction 1 and 1 over 8 feet, and height of fraction 1 and 1 over 5 feet. What is the volume of the carton?

Answers

Answer:

V = 3.6 ft³

Step-by-step explanation:

The formula of a volume of rectangular prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have

[tex]l=2\dfrac{2}{3}\ ft=\dfrac{(2)(3)+2}{3}\ ft=\dfrac{8}{3}\ dt\\\\w=1\dfrac{1}{8}\ ft=\dfrac{(1)(8)+1}{8}\ ft=\dfrac{9}{8}\ ft\\\\h=1\dfrac{1}{5}\ ft=\dfrac{(1)(5)+1}{5}\ ft=\dfrac{6}{5}\ ft[/tex]

Substitute:

[tex]V=\left(\dfrac{8}{3}\right)\left(\dfrac{9}{8}\right)\left(\dfrac{6}{5}\right)=\dfrac{432}{120}=3.6\ ft^3[/tex]

Answer:

3 3/5

Step-by-step explanation:

covert mixed fractions to improper fractions

2 2/3 becomes 8/3

1 1/8 becomes 9/8

1 1/5 become 6/5

then you multiply across will give you 432/120

since the numerator os greater than the demoninator, you have to divide 432

into 120 which then will give you 3 72/120. When you simplify the fraction the final answer is 3 3/5.

What similarity statement can you write relating the three triangles in the diagram ?

Answers

answer is B.
triangle RST ~ triangle RUS ~ triangle SUT

The similarity statement that can be written is;

D(RST) ~ D(RUS) ~D(SUT)

Discussion:

The triangles as represented are right-angled triangles.

In essence, they all have one of their angles to be 90°.

The similarity statement therefore involves the right-angles and is thus; D(RST) ~ D(RUS) ~D(SUT)

Answers

The bill for the month is $87.50, including $40 for 600 minutes and $47.50 for 190 extra minutes.

To calculate the bill for the month, we need to consider the fixed monthly charge and the additional charge for the extra minutes used beyond the 600-minute limit.

Step 1: Calculate the additional minutes used beyond the 600-minute limit:

Total minutes used - Included minutes = Extra minutes

790 minutes - 600 minutes = 190 extra minutes

Step 2: Calculate the additional charge for the extra minutes:

Extra minutes × Additional charge per minute

190 minutes × $0.25/minute = $47.50

Step 3: Add the fixed monthly charge to the additional charge for the extra minutes:

Fixed monthly charge + Additional charge for extra minutes

$40 + $47.50 = $87.50

So, the bill for the month is $87.50.

CAN I GET SOME HELP (RIGHT ANSWER)

Answers

it can be found using the formula 1/2 |major arc - minor arc|

1/2 |105 - 23|
1/2 |82|
41

105-23= 82
82/2= 41
An easier way :)

A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 14 inches,and the bicycle wheel mkes 3 full rotations before stopping. How long is the trace of water on the floor?

Answers

radius = 14 inches
one round of the tire = [tex]2 \pi r[/tex]
one round of the tire = [tex]2 \pi (14)[/tex]
one round of the tire = 87.96 inches
three rounds of the tire = 87.96 x 3 = 263.89 inches

Three of the angles of a quadrilateral are 120° 48° and 92° what is the size of the fourth angle

Answers

360-120-48-92=100°

Each quadrilateral has 360° so simply deduct the angles to get your result.

Hi there! A quadrilateral has angles that add up to 360°. So we have the measurements of the first three angles. We will look for the 4th angle by solving. Let's add the totals of the first 3 angles. 120 + 48 + 92 is 260. Now, we subtract that number from 360. 360 - 260 is 100. There. The measurement of the fourth angle is 100°.

if a + b = -5 and x + y = -5, what is 6y + 6x - b - a

Answers

6(x +y) -(a +b) = 6(-5) -(-5)
= -25

The line plot shows the measurement of a certain liquid (in milliliters) in nine beakers. If you combined the liquids and then put an equal amount of liquid in each beaker, how much liquid would be in each beaker?
A)
1/8 ml

B)
1/2 ml

C)
7/29 ml

D)
1/4 ml

Answers

There would be 1/2 mL in each beaker.

We start by adding the amounts given by the line plot:
1/4 + 1/4 + 3/8 + 3/8 + 1/2 + 1/2 + 5/8 + 3/4 + 7/8

Find a common denominator. The smallest thing that 2, 4 and 8 will all evenly divide into is 8:

2/8 + 2/8 + 3/8 + 3/8 + 4/8 + 4/8 + 5/8 + 6/8 + 7/8

Add the numerators:
36/8

Now we divide this by 9:
36/8 ÷ 9 = 36/8 ÷ 9/1 = 36/8 × 1/9 = 36/72 = 1/2

Find the value of side A on the right triangle, given that side B = 12 cm and side C = 15 cm

Answers

{a}^{2} + {b}^{2} = {c}^{2} [
15-12=3
3sqared=9

A=9

How many ways are there to pick 8 balls from large piles of (identical) red, white, and blue balls plus 1 pink ball, 1 lavender ball, and 1 tan ball?

Answers

Suppose order does not matter, then combinations will consist of 0 to 3 of the singleton colors, and 5 to 8 that are some combination of red, white or blue. This implies that we shall formulate the answer as the sum from k=0 to k=3 of:
N=(Number of ways to pick k of the single colors)*(number of ways to pick 8-k balls from red, white pr blue)
The first factor is C(3,k), let's call the second factor A(8-k), where A(n) is the number of combinations or red, white or blue when n balls are selected. Given that we want to express A(n) as a formula in terms of n, let's say there are r red balls in a combination (0≤r≤n). Then there are (n-r) balls that are either white or blue that have been left over. Thus, the number of white balls must be integer from 0 to (n-r), for the universe of (n-r+1) possibilities. Hence, the rest are blue in exactly one way, so A(n) is the sum over r=0 to n:

A(n)=∑(1+n-r)
A(n)=(n+1)(n+1)-n(n+1)2
=(n+1)(2n+2-n)/2
=(n+1)(n+2)/2

thus
A(5)=6*7/2=21
A(6)=7*8/2=28
A(7)=8*9/2=36
A(8)=9*10/2=45

The total will give:
N=C(3,0)*A(8)+C(3,1)*A(7)+C(3,2)*A(6)+C(3,3)*A(5)
N=1*45+3*36+3*28+1*21=258

The answer is 258

Ewan makes chess boards from wood. Each board has three different kinds of wood. He has five kinds of wood it is workshop maple, cherry walnut, Poplar and birch how many different types of chess board can he make?

Answers

He can make 10 different types of boards.

This is a combination of 5 objects chosen 3 at a time:

[tex]_nC_r=\frac{n!}{r!(n-r)!} \\ \\_5C_3=\frac{5!}{3!2!}=\frac{120}{12}=10[/tex]

Answer:

D.10

Step-by-step explanation:

Billy is creating a rectangular patio in his backyard using square cement tiles. The length of the patio, in feet, is represented by the function l(x) = x + 5, and the width of the patio is represented by the function w(x) = x + 3. Write the standard form of the function which describes the total area of the patio, a(x) in terms of x, the side length of each tile.

Answers

The area of a rectangle by definition is given by:
a = (l) * (w)
Where,
w: width
l: long
Substituting the values we have:
a (x) = (x + 5) * (x + 3)
Rewriting:
a (x) = (x ^ 2 + 3x + 5x + 15)
a (x) = x ^ 2 + 8x + 15
Answer:
The standard form of the function which describes the total area of the patio, a (x) in terms of x is:
a (x) = x ^ 2 + 8x + 15

To find the function for the total area of Billy's patio, a(x), we multiply the length function, l(x) = x + 5, by the width function, w(x) = x + 3. Expanding this multiplication gives us the standard form a(x) = x² + 8x + 15.

Billy is creating a rectangular patio in his backyard using square cement tiles. The function for the length of the patio is l(x) = x + 5, and the function for the width is w(x) = x + 3. To find the function that describes the total area of the patio, a(x), in terms of x, we can multiply the length function by the width function.

First, let's define the area of a rectangle as the product of its length and width: a = l x w. Substituting our functions in, we get:

a(x) = (x + 5) x (x + 3)

Now we will expand this to write it in standard form:

a(x) = x² + 3x + 5x + 15
a(x) = x² + 8x + 15

Therefore, the standard form of the function describing the total area of the patio in terms of x, the side length of each tile, is a(x) = x² + 8x + 15.

Which is the best definition of a square? A. a 4-sided polygon with all sides equal B. a parallelogram with all sides equal and all angles equal C. a combination of a rectangle and a trapezoid D. a 4-sided polygon with all angles equal

Answers

I would say B) A parallelogram with all sides equal and all angles equal. Parallelograms aren't all squares. They can be rectangles and rhombuses. I would say B. They all have the same lengths on all sides. They all have the same angles as well. Take a look at the pictures below. They are all parallelograms. All sides are the same, and all angles are the same.

Hello,

The answer should be option B "a parallelogram with all sides equal and all angles equal".

Reason:

The answer is option B because a square is a parallelogram with all sides and angles equal. Its not option A because a square is not a polygon but does have equal sides. Its also not option C because a square is a rectangle but not a trapezoid therefore not combined. Its also not option D because its not a polygon but does have four sides which saying there not equal therefore not the answer.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

According to the south carolina department of mental health web site, for every 200 u.s. women, the average number who suffer from anorexia is one. a group of 600 u.s. women is randomly chosen. part (a) correct: your answer is correct. part (b) correct: your answer is correct. part (c) how many are expected to suffer from anorexia

Answers

3 are expected to have the condition.

The expected value is the found by multiplying the probability by the number in the sample:

(1/200)×600
= (1/200)×(600/1)
= (1×600)/(200×1)
= 600/200 = 3

Suppose that you have a goal to drive two miles at an average rate of 60 miles per hour (mph). during the first mile you travel at a rate of 30 mph. how fast would you need to travel during the second mile in order to reach your goal of 60 mph for the total two mile distance? (hint: remember that rate is found by taking distance divided by time.)

Answers

Your goal requires you complete the distance in 2 minutes. If you travel at half the target speed, you will have used up the allowed time traveling the first half of the distance.

You need to travel the second mile at infinite speed to average 60 mph.

One kilometer equals 0.62 miles. How many kilometers equal 16 miles? Round the answer to the nearest tenth. 2.6 kilometers
9.9 kilometers
25.8 kilometers
99.2 kilometers

Answers

25.8 kilometers that is the answer to your question

Answer: 25.8 kilometers

Step-by-step explanation:

Given: One kilometer = 0.62 miles

Then, [tex]1\text{ mile}=\dfrac{1}{0.62}\text{ kilometers}[/tex]

Then to find the number of kilometers in 16 miles, we need to multiply 16 to [tex]\dfrac{1}{0.62}[/tex], we get

[tex]\text{ 16 miles =}16\times\dfrac{1}{0.62}=25.806451612\approx25.8\text{ kilometers}[/tex]

Hence, 25.8 kilometers equals to 16 miles.

which least to greatest 125% 6/5 1.22

Answers

6/5, 1.22, 125%

Hope I helped!

Let me know if you need anything else!

~ Zoe (Rank:'Genius')

Final answer:

To compare the numbers 125%, 6/5, and 1.22, they were all converted to decimal form which revealed the least to greatest order as 1.22, 6/5, and 125%.

Explanation:

To arrange the numbers 125%, 6/5, and 1.22 from least to greatest, we first need to express all of them in the same format for an accurate comparison. Let's convert each number to a decimal:

125% as a decimal is 1.25 (since 100% is equal to 1, hence 125% is 1.25).6/5 as a decimal is 1.2 (6 divided by 5 equals 1.2).1.22 is already in decimal form.

Now, we can easily compare:

1.226/5 (1.2)125% (1.25)

The arrangement from least to greatest is 1.22, 6/5, 125%.

Javier buys 12 bagels for $2.50. At this rate how many bagels could Javier buy for $6.25?

A. 18
B. 30
C. 31
D. 48

Answers

He can buy 30 bagels.
2.50/12=0.21
Each is about $.21.
6.25/.21=29.9=30

That means Javier can buy 30 bagels.

Hope this helped☺☺

the answer could possible be c

Five years ago, Tim’s mom was three times Tim’s age today. Now their combined ages are 45. How old is Tim’s mom today?

Answers

To solve this problem, you must name a variable, create expressions representing the parts of the problem, and then set up an equation.

Let Tim's age today be t. Since Tim's mom's age five years ago was 3 times Tim's current age, Tim's mom's current age is equal to 3t + 5.
Their ages are collectively 45, so Tim's age t and Tim's mom's age 3t + 5 must be equal to 45. Set up an equation and solve for the variable t.

45 = t + (3t + 5)
45 = t + 3t + 5
45 = 4t + 5
40 = 4t
10 = t

Tim is currently 10, and after plugging 10 for t into 3t + 5, we see that Tim's mom is 35.

Now let's check our work. Their combined ages are 45; 10 plus 35 is equal to 45, so that is correct. Further, addressing the "Five years ago, Tim's mom was three times Tim's age today" bit, we see that 10 - Tim's current age - times 3 is equal to 30, which would be Tim's mom's age 5 years ago.

Answer:
Today, Tim's mom is 35.

Answer:

35 years

Step-by-step explanation:

45 = t + (3t + 5)

45 = t + 3t + 5

45 = 4t + 5

40 = 4t

10 = t

3*10=30,

30+5=35

Three cards are drawn from a deck without replacement. what is the probability that all three cards are clubs?

Answers

b.0.0129 is the answer

Rules for multiplying and dividing by 1 and 0

Answers

Mutiplying: the product is always 0

Multiplying anything by 1 is always the number your multiplying it by so for example 1*2=2

cody has $700 in a savings account that pays 4% simple interest how much will he have in one year

Answers

28$$$$$$$$$$$$$$$$$$$$

700(1.04)= $728 the 700 dollars is multiplied by 1.04 to get 728

A jar contains 26 fluid ounces of spaghetti sauce. How many cups of spaghetti sauce do 4 jars have

Answers

we know that
1 ounces------------------> is 0.125 cup

if one jar contains------------------> 26 ounces of spaghetti sauce
4 jars---------------------------------> X
X=4*26-----------> 104 ounces

if one ounce---------------> 0.125 cup
104 ounces----------------> X
X=104*0.125-----------> 13 cups

the answer is 13 cups

A pitcher contains 3 1/2 pints of lemonade. Susan pours 5/8 of a pint into a glass, and Mateo pours 1/2 pint into a glass. How much lemonade is left in the pitcher?

Answers

we have 3 1/2 pints of lemonade
3 1/2- 1/2 (Mateo)=3
3- 5/8= 2 8/8- 5/8=2 3/8 lemonade left

Who topping covers more of the pizza 2/8 or 5/8

Answers

Hello,

The answer should be "5/8".

Reason:

My teacher taught me that the fractions with the smaller numbers is the greater number than the fraction with bigger numbers therefore your answer is 5/8!

2/8 < 5/8

Therefore its greater topping.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

5/8ths because it is larger number and if you change it into a a decimal then they would be 2/8 = 0.25
5/8 = 0.625
between these two numbers 0.625 is the largest and hence 5/8 covers more toppings than 2/8 does.

I love cheese pizza

which describes the correlation shown?

Answers

Answer:

The correlation that is shown in the scatter plot is:

Strong positive.

Step-by-step explanation:

From the scatter plot we see that with the increase of one variable the second variable also increases.

Hence, the association is positive.

Also, if we draw a trend line that best represents the scatter plot then not all the points will lie above the line but all the data points are either over the line or very close to the line this means that the correlation coefficient is close to 1 but not exactly equal to 1.

Hence, the correlation is:

Strong positive.

( For perfect positive all the data points should lie above that line i.e. correlation coefficient must be equal to 1)

Answer:

Option C) Strong positive

Step-by-step explanation:

Correlation

Correlation is a technique that help us to find or define a relationship between two variables. It is a measure of linear relationship between two quantities. A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases.

Looking at the graph it could be said that the variables are strongly positively correlated as with a small increase in one variable, the other variable increases.

It is not a perfect positive relation as change in one variable does not lead to equal change in other variable.

It cannot be negative relation as well.

The perimeter of a rectangle is 80 feet. Find the demensions if the length is 5 feet longer than four times the width. Then find the area of the rectangle.
-Show All Work!-

Answers

Hey there!

The first thing we should do is review the formulas for area and perimeter.
Perimeter can be expressed in two ways: a) l+w+l+w OR b) 2l+2w.
The formula for area is: l*w

We know that the length is 5 feet longer than the width, so when we're defining our variables we can say that width is equal to 'w', and length is equal to 4w+5.
Since we know that the perimeter is equal to 80, we can say that [tex]80= 2(4w+5) + 2(w)[/tex].

Now all we have to do is combine like terms and solve for 80:

[tex]80 = 2(4w+5) +2w [/tex]
[tex]80 = 8w + 10 +2w[/tex]
[tex]80 = 10w +10[/tex]
[tex]80-10 = 10w +10 -10[/tex]
[tex]70 = 10w[/tex]
[tex] \frac{70}{10} = \frac{10w}{10} [/tex]
[tex]7 = w[/tex]

We now know that the width is equal to 7 feet. To find the length, we can substitute the width into 4w+5:
[tex]l = 4w + 5 = 4(7)+5[/tex]
[tex]l = 28 + 5[/tex]
[tex]l = 33[/tex]

Now we know that the length is equal to 33 feet.

So there's your dimensions: 7ft by 33 ft.

Next, to find the area, we take l*w
[tex]33*7 = 231ft^{2} [/tex]

Hope this is helpful! If any of this doesn't make sense or there's more I can help with, please let me know!

Mike used a rectangular prism and two cubes to create a model bench for his class project as shown below.

What is the surface area of the model bench?

A. 850 sq in
B. 800 sq in
C. 750 sq in
D. 700 sq in

Answers

surface area = 2(wl + hl + hw)

top section 2(5*25 + 5*25 + 5*5) = 550

lower part = 2(5*5 + 5*5 + 5*5) = 150

150 + 150 + 550 = 850

answer is A

I need to collect data for this table please someone help

Answers

Total number of people living in an apartment = 18 + 36 = 54
18 people living in an apartment have a pet.

So percentage of people living in an apartment who have a pet = [tex] \frac{18}{54}*100=33 [/tex]%

Total number of people living in a house = 43 + 24 = 67
43 people living in a house have a pet.

So percentage of people living in a house who have a pet = [tex] \frac{43}{67}*100=64 [/tex]%

So answer in first blank is 33% and answer in second blank is 64%.

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