find the derivative of g(x)=secx/(x+1)^3

Answers

Answer 1

Given data:

The given function is g(x)=secx/(x+1)^3.

The expression for the derivative of the function is,

\(\begin{gathered} \frac{d}{dx}g(x)=\frac{d}{dx}\frac{\sec x}{(x+1)^3} \\ \text{ =}\frac{(x+1)^3\frac{d}{dx}(\sec x)-\sec x\frac{d}{dx}(x+1)^3}{\lbrace(x+1)^3\rbrace^2} \\ =\frac{\sec x\tan x(x+1)^3-3(x+1)^2\sec x}{(x+1)^6} \\ =\frac{(x+1)^2\lbrace\sec x\tan x(x+1)^{}-3^{}\sec x\rbrace}{(x+1)^6} \\ =\frac{\sec x\tan x(x+1)^{}-3^{}\sec x}{(x+1)^4} \\ \\ \end{gathered}\)

Thus, the derivative of the giiven function is (secxtanx(x+1)-3sex)/(x+1)^4.


Related Questions

PLSS Someone plss help plss helppp plllsss Will mark brainliest!!!

PLSS Someone plss help plss helppp plllsss Will mark brainliest!!!

Answers

Answer:

( 6 , 8 )

Step-by-step explanation:

y = kx

k = \(\frac{y}{x}\)

( 3 , 4 )

k = \(\frac{4}{3}\)

\(\frac{4}{3}\) = \(\frac{8}{6}\) = \(\frac{12}{9}\) = ....

( 6 , 8 )

Jose can run 1 miles in 1/6 of
an hour. How far can he run
in one hour?

Jose can run 1 miles in 1/6 ofan hour. How far can he runin one hour?

Answers

Answer:

He can run 8 miles in one hour.

Step-by-step explanation:

We have,

Jose can run 1 1/3 miles in 1/6 of  an hour.

We need to find how far he can run in one hour.

\(1\dfrac{1}{3}\ \text{miles}=\dfrac{1}{6}\ \text{hour}\)

Now using unitary method,

\(1\ \text{hour}=\dfrac{4}{3}\times 6\ \text{miles}\)

or

\(1\ \text{hour}=8\ \text{miles}\)

So, he can run 8 miles in one hour.

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one
baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has
no effect, so the probability of a girl is 0.5. Assume that the groups consist of 45 couples. Complete parts (a) through (c)
below.

Assume that different groups of couples use a particular method of gender selection and each couple gives

Answers

a) The value of the mean is μ = 22.5

   The value of the standard deviation is σ = 3.5

b) The Value of 15 girls or fewer is significantly low.

   The value of 30 girls or more is significantly high.

c) The result 36 is significantly high because 36 is greater than 30 girls. A         result of 36 girls is not necessarily definitive proof of the method's effectiveness.

What is the standard deviation?

The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.

According to the given information

a) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.

Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.

The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:

μ = np = 45 x 0.5 = 22.5

Therefore, we expect to see around 22-23 girls in a group of 45 couples.

The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:

σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535

Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.

b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.

Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.

Significantly high:

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Significantly low:

Mean - 2σ = 22.5 - 2(3.535) = 15.43

c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.

This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.

It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.

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2x+ 5y = 15
5x+10y = 35
O A. (5.-1)
O B. (5,1)
(
O C. (10,-1)
O D. (10,1)

Answers

Answer:

B.

Step-by-step explanation:

Plug in those x and y values into your equations.

(x, y) = (5, 1)

2x + 5y = 15

2(5) + 5(1) = 15

10 + 5 = 15

5x + 10y = 35

5(5) + 10(1) = 35

25 + 10 = 35

This proves those values are true. So the answer is B.

Which of the following is not a way of generating random numbers? A. random number tables B. using phone numbers selected at random in a local phone book C. using the internet D. books of random numbers

Answers

Answer:

well all of these look like a way so we have to use elimination method

A : random number tables : well it has random numbers so X out

B: PHONE NUMBERS: well phone numbers are random so X out

C: USing the internet : totally X out

D: books of random numbers: X out

so none of the above i guess

The only way that might not be used in generating random numbers is : (B). using phone numbers selected at random in a local phone book

Meaning of random numbers

Random numbers are numbers that occurs randomly without prediction. these numbers are impossible to predict using past values.

Random numbers are important for computer encryption and lotteries.

In conclusion, The only way that might not be used in generating random numbers is using phone numbers selected at random in a local phone book

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Help I'll mark brainliest

Help I'll mark brainliest

Answers

Answer:

a

Step-by-step explanation:

the product of -3/4 and a namber x is -27​

Answers

Answer:

36

Step-by-step explanation:

crossing out the 2 negatives, simplifying

3/4x=27

plz brainliestt

Corrine is purchasing beads to make a new necklace and bracelet set. The two pieces of jewelry each need silver and green beads. The necklace requires 25 silver beads and 15 green beads. The bracelet requires 10 silver beads and 5 green beads. Corrine paid $27.50 for the necklace beads and $10 for the bracelet beads. How much does each silver bead cost? How much does each green bead cost? Be sure to show your work and explain your answer.

Answers

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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Find the perimeter for a rectangle that has an area of 2x^2+6x-8 and length of 2x-2. (Hint: First find the length)

Answers

The question is a mistake the value of length is either zero or negative which cannot be possible.

If there is an outlier should we report mean or median?

Answers

Answer:

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers.

Step-by-step explanation:

Answer:

If there is an outlier you should report the median. This is because the value of a mean can be distorted by the outliers. So, you can use the median when the distribution is not symmetrical.  

Step-by-step explanation:

Find the cost paid for the loan. $2400 at 10.5% for 5 years

Answers

Answer:

Step-by-step explanation:

Answer $1260

1 + tan ( θ ) ÷ 1 − sin ( θ ) = ( tan ( θ ) + csc ( θ ) 2

Answers

Answer:

4655

Step-by-step explanation:

this is not correct question because I know that is omath question

Solve the following equation. Then place the correct number in the box provided. 2x - 1 ≤ x + 5

Answers

\(\huge\textbf{TheStarryNights }\)Hi There!

Solve the Inequality:

2x-1≤x+5

Move all the variables (in this case, x's) to the left, using the opposite operation:

2x-x-1≤5

Move -1 to the left:

2x-x≤5+1

Combine like terms:

x≤6 (Answer)

Hope it helps & enjoy your day!

\(\huge\textbf{TheStarryNights}\)

please help asap (answer only if you know the question)​

please help asap (answer only if you know the question)

Answers

The Equation of bisector 5x-7y+3=0 which is a straight line.

What is bisector?

A straight line that divides an angle of a triangle in equal value.

What is perpendicular bisector?

The line that lies perpendicular to a side and goes through the midpoint of its length.

Given, coordinate H (-7,2), K (3, -4) and L (5,4)

we plot a triangle HKL with this point.

midpoint of side HK is found by (-7+3)/2 and (2-4)/2

hence, midpoint of HK is (-2,-1) is denoted by P

the perpendicular bisector of side HK means a straight line from the midpoint of HK to the point L(5,4). The bisector line PL divide the angle HLK.

so, the equation of bisector is y-y₁ = (y₂-y₁)/(x₂-x₁)[x-x₁] because the bisector line passes through the point P(-2,-1) and L(5,4)

  y-(-1) = [4-(-1)]/[5-(-2)]× [x-(-2)]

y+1 = 5/7×(x+2)

7y+7= 5x+10

5x-7y+3=0

hence, the equation of bisector is 5x-7y+3=0

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Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square​

Answers

There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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Compare the best estimate for 1.789/178 and 0.05. Which is less?

Answers

Answer:

The smaller number in 0.01

Step-by-step explanation:

To find this answer, just take the fraction and find the quotient of both numbers.

1.789/178 = 0.01005056179

Now take the quotient and compare it to 0.05.

Is 0.01 larger or 0.05 - the answer is 0.01.

What value of X guarantees that BC || DE?

Answer Choices:

1, 4, 5, 6.25

help me out :) & feel free to add an explanation <3

What value of X guarantees that BC || DE? Answer Choices: 1, 4, 5, 6.25help me out :) &amp; feel free

Answers

Answer:

4

Step-by-step explanation:

as BC║DE

so, AD:BD=AE:CE

   or, CE=(BDₓAE)/AD

   or, x=(5×16)/20=4

An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be​ 95% confident that the sample mean is within 4 IQ points of the true mean.

What is the required sample size?

Answers

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

I need help asappppppp

I need help asappppppp

Answers

Answer:150?

Step-by-step explanation:

What percent is 11÷88

Answers

Answer:

hello

Step-by-step explanation:

it must be 0,125

hope it helps

Explain how adding and subtracting decimals is similar to adding and subtracting whole
numbers. Explain how they are different.

Answers

Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit

How to illustrate tye decimal?

One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.

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Right triangle with a hypotenuse of 159 ft and Angle A = 34 degree
Calculate the length of the sides they should be rounded to the nearest whole foot. The rounded for the legs (side) should be used to calculate the area of the triangle

Answers

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Petra jogs 6 miles in 42 minutes. At this rate, how long would it take her to jog 10 miles?

Answers

Answer:

70 minutes

Step-by-step explanation:

So if Petra takes 42 min to jog 6 miles, then how long would it take to jog 10 miles? What do we do?

We make a proportion, 6/42 = 10/x

We cross multiply and get an equation of 10*42 = 6*x

We simplify, 6x = 420

And divide 6 by both sides to get x= 70 min

- Hope this helped :)

Brainliest is most appreciated :)

Answer:

It would take Petra 70 minutes to jog 10 miles.

Step-by-step explanation:

There are several ways we can solve this.

As a rate:

42/6=7

One mile takes her 7 minutes.

7*10=70

10 miles takes her 70 minutes.

As a proportion:

6/42=10/x

Cross multiply.

420=6x

x=70

It would take her 70 minutes.

lukes house is located at the point shown on the coordinate grid. kyles house is located 4 units left and 2 units up from lukes house plot a point on the coordinate grid to represent the location of kyles house.

Answers

The coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the Coordinates of Luke's house on the coordinate grid.

The grid representing Kyle's house. However, based on the given information, we can determine the coordinates of Kyle's house relative to Luke's house.

If Luke's house is located at the point (x, y), then Kyle's house is located 4 units to the left of Luke's house, which means the x-coordinate of Kyle's house is (x - 4). Similarly, Kyle's house is located 2 units up from Luke's house, which means the y-coordinate of Kyle's house is (y + 2).

Therefore, the coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the coordinates of Luke's house on the coordinate grid.

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lukes house is located at the point shown on the coordinate grid. kyles house is located 4 units left

HELP!!!!
What is the result when the number 80 is decreased by 8%?

Answers

Answer:

79.92

Step-by-step explanation:

Step-by-step explanation:

80 decreased by 8% means;

80 - (8/100 × 80) = 80 - (0.8 × 8)

= 80 - 4.8 = 75.2

Anyone knows what the answer for this is I am really confused on it

Anyone knows what the answer for this is I am really confused on it

Answers

By replacing x in the equation with -1 our result will be 1.5. So f(-1)=1.5

Define the binary operator ∇ by: a ∇ b = 4 Simplify each of the following. Do the order of operations (do what is in parentheses first). ( 4 ∇ 3 ) ∇ 6 = ( 7 ∇ 2 ) ∇ 5 =

Answers

Given that a ∇ b = 4, it doesn't matter what values you choose for a and b, the result of the ∇ operation is always 4.

So, unless your question is missing some additional details, we have

(4 ∇ 3) ∇ 6 = 4 ∇ 6 = 4

and

(7 ∇ 2) ∇ 5 = 4 ∇ 5 = 4

Referring to the figure, which inequality is shown in

the graph.

a. y ≤ √4x + 8

b. y > √4x + 8

c. y < √4x + 8

d. y 2 √4x + 8

Ay

O

Referring to the figure, which inequality is shown inthe graph.a. y 4x + 8b. y &gt; 4x + 8c. y &lt; 4x

Answers

Referring to the figure, an inequality which is shown in the graph include the following: \(y \leq \sqrt{4x+8}\).

What is a square root function?

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N).

Where:

N represents an integer.g(x) and f(x) represent functions.

Therefore, the required square root function can be obtained by applying a vertically stretching the parent square root function by a factor of 4 as follows;

f(x) = √x

\(y \leq \sqrt{4x+8}\)

In conclusion, a less than or equal to inequality symbol must be used because the solid line is shaded below.

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description of set D={3,6,9,12,15}

Answers

Answer:

The set D has 5 elements - 3, 6, 9, 12, and 15, all of which are multiples of 3.

This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year

Answers

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

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