find the derivative of sinx/1+cosx, using quotient rule​

Answers

Answer 1

Answer:

f'(x) = -1/(1 - Cos(x))

Step-by-step explanation:

The quotient rule for derivation is:

For f(x) = h(x)/k(x)

[tex]f'(x) = \frac{h'(x)*k(x) - k'(x)*h(x)}{k^2(x)}[/tex]

In this case, the function is:

f(x) = Sin(x)/(1 + Cos(x))

Then we have:

h(x) = Sin(x)

h'(x) = Cos(x)

And for the denominator:

k(x) = 1 - Cos(x)

k'(x) = -( -Sin(x)) = Sin(x)

Replacing these in the rule, we get:

[tex]f'(x) = \frac{Cos(x)*(1 - Cos(x)) - Sin(x)*Sin(x)}{(1 - Cos(x))^2}[/tex]

Now we can simplify that:

[tex]f'(x) = \frac{Cos(x)*(1 - Cos(x)) - Sin(x)*Sin(x)}{(1 - Cos(x))^2} = \frac{Cos(x) - Cos^2(x) - Sin^2(x)}{(1 - Cos(x))^2}[/tex]

And we know that:

cos^2(x) + sin^2(x) = 1

then:

[tex]f'(x) = \frac{Cos(x)- 1}{(1 - Cos(x))^2} = - \frac{(1 - Cos(x))}{(1 - Cos(x))^2} = \frac{-1}{1 - Cos(x)}[/tex]


Related Questions

heyy! i’ll give brainliest please help.

Answers

The answer is a for this question

What is the surface area of the rectangular prism shown by net?

Answers

The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

The radius of a circle is 6 feet. What is the circle's circumference? Use 3.14

Answers

I think you divide so 1.91

Help me plz thank you

Answers

Answer:C

Step-by-step explanation: 100 x 23/100=23

Phillip watched a beach vollyball game from 1 p.M. To 1:15 p.M How many degrees did the minute hand turn?

Answers

Answer: 90°

Step-by-step explanation:

A full rotation on a clock would be 360° like a normal circle and this would represent a full hour.

When it comes to 15 minutes therefore, to find the number of degrees the time would turn, find out the proportion of an hour that 15 minutes is then relate it to 360°.

= 15 mins / 60 mins

= 1/4 hours

If an hour is 360°, 1/4 hours must be:

= 1/4 * 360

= 90°

The restaurant manager wants to find how much they are spending for pies and cakes. Last week they payed 204$ for 12 pies and 8 cakes

Answers

Answer: See explanation

Step-by-step explanation:

Your question isn't complete and I couldn't get the exact question online but let's reframe it and solve it.

The restaurant manager wants to find how much they are spending for pies and cakes. Last week they payed 204$ for 12 pies and 8 cakes. This week, they paid $129 for 5 pies and 7 cakes.

Let's say the cost of pies is x

Let's say the cost of cake is y.

We'll then use the information given to make an equation which will be:

Last week they payed 204$ for 12 pies and 8 cakes. This will be:

12x + 8y = 204........ i

This week, they paid $129 or 5 pies and 7 cakes. This will be:

5x + 7y = 129 ........... ii

Therefore,

12x + 8y = 204........ i

5x + 7y = 129 .......... ii

Multiply equation i by 5

Multiply equation ii by 12

60x + 40y = 1020 ....... iii

60x + 84y = 1548 ........ iv

Subtract iii from iv.

44y = 528

y = 528/44

y = 12

The cost of cake is $12.

From equation i,

12x + 8y = 204

12x + 8(12) = 204

12x + 96 = 204

12x = 204 - 96

12x = 108

x = 108/12

x = 9

The cost of pies is $9.

My brain is not cut out for this. Plz help lol.

Answers

Answer:

Step-by-step explanation:

It’s c

Determine the sample space of all of the possible outcomes of choosing a card numbered 1,
2,3 or 4 and a blue, green, or yellow marble. How many outcomes involve choosing a blue
marble?

Answers

Answer:

1/3

Step-by-step explanation:

sample space includes 12 outcomes:

blue, green, yellow for 1, 2, 3, and 4

P(blue) = 4/12 or 1/3

!!!!NEED HELP ASAP!!!! NO LINKS OR REPORT

Answers

Answer:

y = 3x - 5

Step-by-step explanation:

So first take any two points from the graph.

(0, -5), (2, 1)

The slope is [tex]\frac{1 + 5}{2 - 0} =3[/tex]

y = mx + b

b is the y intercept

The y intercept is (0, -5) as this is where the line intersects the y axis.

y = 3x - 5

2) Mass of the earth is 5976000000000000000000000 kg and that of Uranus is 86800000000000000000000000 kg , which one has greater mass ? and how much ? compare in exponential form.​

Answers

Step-by-step explanation:

mass of earth=5.976×10^24 and

mass of Uranus =8.68×10^25

the mass of

Uranus is greater than that of the Earth by comparing its power 10

The mass of Uranus is greater than that of the Earth by comparing its power 10

What is an exponential form of 10?

It is a shortcut way of writing repeated multiplication involving base and exponents. For example the 3 in [tex]10^{3}[/tex] is called the exponent. The expression [tex]10^{3}[/tex] is called exponential expression.

Given

Mass of the earth = 5976000000000000000000000 kg

Rewrite in exponential form

Mass of the earth = 5.976×10^24

Mass of Uranus = 86800000000000000000000000 kg

Rewrite in exponential form

Mass of the Uranus = 8.68×10^25

∴ 8.68 × [tex]10^{25}[/tex] > 5.976 × [tex]10^{24}[/tex]

We can clearly say that by seeing the exponential form of masses of earth and Uranus i.e.,

The mass of Uranus is greater than that of the Earth by comparing its power 10.

Learn more about exponential form of 10 here

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Evaluate the piece wise function for the given values of x by matching the domain values to the range values.

Domain values
x=1 f(x)=

x=3 f(x)=

x=5 f(x)=

x=12 f(x)=

x=15 f(x)=

Answers

Answer:

when

x=1 then f(x)= -5

x=3 then f(x)= 2

x=5 then f(x)= 18

x=12 then f(x)= 15

x=15 then f(x)= 13

Step-by-step explanation:

AREA OF A CIRCLE HELP PLS​

Answers

Answer:

153.86 in²

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex]

d = 14 inches, r = d/2 = 7 inches

= 3.14 * 7 * 7

= 153.86 in²

-4x > 500...........................................

Answers

-4x > 500
Divide -4 on both sides.

(Now this is very important, whenever you divide OR multiply an equality by a NEGATIVE number the sign will ALWAYS flip.)

x < -125


~

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism.The company wants to use the package that has the least amount of wasted space. The company should choose

Answers

Answer:

The Company should choose to get the cylinder packages  ( V = 42.39 in³ )

Step-by-step explanation:

The volume of a cylinder of radius of circumference 1.5 in  and h = 1.5*4

h  =  6 in   is:

V(c)  =  π *r²*h   =  π * (1.5)²*6   =   π *2.25*6

V(c)  = 42.39 in³

Now V(p) =  Square of the base ( of side 3 in) * h

h  =  6 in

V(p)  =  (3)²*6

V(p)  =  54 in³

If we compare these two volumes we see that the volume of the cylinder is small than that of the square prism

Greata had a price of cloth that is 9 yards long. She cuts it into prices that are each 1/3 yard long. How many prices of cloth does Greata have now?

Answers

Given:

Length of cloth = 9 yards

Length of pieces = [tex]\dfrac{1}{3}[/tex] yards each

To find:

The number of pieces of cloths after cutting.

Solution:

Let n be the number of required pieces.

Length of each piece is [tex]\dfrac{1}{3}[/tex] yards. So, the length of n pieces is [tex]\dfrac{1}{3}n[/tex] yards.

The length of the whole cloth is 9 yards. So, [tex]\dfrac{1}{3}n[/tex] yards must be equal to 9 yards.

[tex]\dfrac{1}{3}n=9[/tex]

Multiply both sides by 3.

[tex]n=9\times 3[/tex]

[tex]n=27[/tex]

Therefore, the Greata have 27 pieces of cloths.

Please help! DO NOT SEND LINK!

Answers

Answer:

Mizuki here to answer!

The correct answer would be 15 inches!

Step-by-step explanation:

7200 ÷ (24 x 20) = 15

Answer:

Hello! answer: 15

Step-by-step explanation:

The volume is 7200 volume is found by doing length × width × height therefore the height is 15 because... 24 × 20 × 15 = 7200 HOPE THAT HELPS!

Determine the equation of the circle graphed below. ​

Answers

Answer:

Step-by-step explanation:

the formula for a circle not on the origin is :

(x−h)^2+(y−k)^2=r^2

for the circle shown it looks like the  circle is centered at (1,3)

then h=1 and k=3 and the radius looks to be about 2

(x−1)^2+(y−3)^2=2^2

(x−1)^2+(y−3)^2=4

there is your equation for that circle shown in the graph

gcf (greatest common factor) of 9ab and 16bc

Answers

the greatest common factor is 1

Answer:

1b or b

Step-by-step explanation:

its verified by my math teacher Mr. Gonzales <3333

Today's cafeteria specials at a high school in Westford are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 13 turkey sandwiches and 69 chef salads, for a total of $151. During the late lunch, 61 turkey sandwiches and 41 chef salads were sold, for a total of $143. How much does each item cost?

Answers

Answer:

chef salads = $2

turkey sandwiches = $1

Step-by-step explanation:

two equations can be derived from the question

13t + 69c = 151 eqn 1

61t + 41c = 143 eqn 2

t = turkey sandwiches

c = chef salads

multiply equation 1 by 61 and equation 2 by 13

793t + 4209c = 9211 eqn 3

793t + 533c = 1859 eqn 4

subtract equation 4 from 3

7352 = 3676c

c =2

substitute for c in equation 1

13t + 69(2) = 151

13t + 138 = 151

13t = 151 - 138

13t = 13

t = 1

PLEASE HELP!!! I really need help with this question, so if anyone could spare a few min then thank you so much!! ;w;

Answers

Answer:

Hello! answer: -6

Step-by-step explanation:

Hope that helps!

Which is the better buy? 16 cards for $12.20 OR 14 cards for $10.90

Answers

Answer:

The better buy is 16 cards for $12.20 because

Step-by-step explanation:

You need to find the individual price for each card in the packet. So first lets do 16 cards for $12.20, you divide $12.20 by 16 to get the price of one card. 12.2/16=0.7625, or about $0.76. Next we do $10.90 divided by 14, 10.9/14=0.7785, or about $0.78, which means 16 cards for $12.20 is the better buy!

Susie flips a coin three times. what is the probability of her getting tails all three times?​

Answers

Answer:

18

Step-by-step explanation:

Hoped this helped!!

Answer:

1/8 or 12.5%

Step-by-step explanation:

It is a 0.5 percent chance of getting tails in a coin flip. Since you flip the coin three times, multiply the probability of getting tails in a coin flip three times. (0.5) Times (0.5) Times(0.5)= 1/8 or 12.5%.

i need help please !

Answers

It’s C I think it is

Answer:

[tex]D.\ 7 \frac{3}{4} * \frac{\sqrt{16} }{5} = \frac{31}{4} * \frac{4}{5} = \frac{31}{5} \\\\C. \ 7 \frac{3}{4} + \frac{\sqrt{16} }{5} =\frac{31}{4} + \frac{4}{5} = \frac{171}{20}[/tex]

The temperature was 70 then dropped to 30 how much is it now?

Answers

Answer:

nmdjskln Jdj

Step-by-step explanation:

Mmh not sure but I think 30

Find the volume of the rectangular prism
Thank you!!

Answers

Answer:90

Step-by-step explanation: do length x base x height to get your answer

please help! i’ll mark you brainlist if it’s correct. it’s probably easy but i’m terrible at math

Answers

Answer: c

Step-by-step explanation:

The 3rd one is in standard form

Find an expression which represents the sum of (-4x + 3) and (8x + 2) in
simplest terms.

Answers

Answer:

4x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

(-4x + 3) + (8x + 2)

Step 2: Simplify

Combine like terms (x):                                                                                    4x + 3 + 2Combine like terms:                                                                                         4x + 5

help me pleaseeeee. what is this?

Answers

Answer:

104

Step-by-step explanation:

all the angles of a triangle add up to 180, so set up an equation like this:

x+35+41=180

now solve for x

x=180-35-41

x=104

104 degrees a triangle = 180 degrees 104 + 41 + 35 = 180 degrees

A man walks 1500 metres.

On a map this is shown as 3cm.

What is the scale on the map?​

Answers

The scale on this map is 1 cm = 500 meters

The scale on the map is 1 cm for 500 m.

What is scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, A man walks 1500 metres. on a map, this is shown as 3 cm.

3 cm = 1500 m

1 cm = 500 m

Hence, The scale on the map is 1 cm for 500 m.

For more references on scale, click;

https://brainly.com/question/841108

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...5, ___, 29, .....

The missing term is ___

Answers

Answer:

17

Step-by-step explanation:

I think the answer is 17 if helpful please mark me brainliest!

Answer:

12

Step-by-step explanation:

see if you do the math you will find out that its 12         17+12=29

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