Find the derivative of the following function:

Find The Derivative Of The Following Function:

Answers

Answer 1

The derivative of the function [tex]f(x) = \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}[/tex] will be given below.

[tex]f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(1.5x^3 + 4x^2 + 2x + 2)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}[/tex]

What is differentiation?

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decrease.

The equation of the function will be given as,

[tex]f(x) = \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}[/tex]

The derivative of the function will be given as,

[tex]f'(x) = \dfrac{d}{dx} \ \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} \\\\\\f'(x) = \dfrac{2 + 2(x^2 + 1)(0.5x^2 + 2x + 1) \cdot (x + 2) + (0.5x^2 + 2x + 1)^2 \cdot 2x}{2\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} }\\\\\\f'(x) = \dfrac{2 + (0.5x^2 + 2x + 1)[2(x^2 + 1)(x + 2) + (0.5x^2 + 2x + 1) \cdot 2x]}{2\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} }\\[/tex]

Solve the equation further, then we have

[tex]f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)[(x^2 + 1)(x + 2) + (0.5x^2 + 2x + 1) \cdot x}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}\\\\\\f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(x^3 + 2x^2 + x + 2 + 0.5x^3 + 2x^2 + x)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}\\\\\\f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(1.5x^3 + 4x^2 + 2x + 2)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}[/tex]

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Related Questions

between 1/4 aand 9/2 which fraction is greater


Answers

Answer: the answer is 9/2

Four friends go to a theater and sit in a row. What is the probability that two of them, Nathan and Violetta, are NOT neighbors?

Answers

Answer: 3/4 im pretty sure

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

When Violetta goes first, their are 4/24 possibilities. Same for Nathan.

The rest are just both 2/24 possibilities. Therefore, the answer is 1/2.

In a small town, the population increased from 25,000 people in 2010 to
32,000 people in 2020. What is the percent increase in population? What is the answer

Answers

Answer:32000 - 25000 =7000 increase percentage = increase amount

Step-by-step explanation:

5:2:11=___:6____
Can you please help me I am stuck

Answers

15:6:33

if you go from 2 to 6, that’s been multiplied by 3, so you now need to times the other numbers by 3

Can someone please help ASAP assignment due tomorrow!
No 4.

Answers

The area of the large square = 9/4 square inches

There is a total of 25 small equally sized squares inside the large square.

The shaded portion given contains 4 such small equally-sized squares. This shaded portion has an area of 9/25 square inches.

We will first find the area of one small sized square and then will use it to find the area of the large square as the large square is made of 25 such small squares.

That is, area of 4 small squares = 9/25

So area of one small square = Area of 4 small squares/ 4

                                               = (9/25)/4

                                               = 9/(25 x 4)

                                               = 9/100 square inches

Now to find the area of the large square, multiply the area of one small square with the total number of small squares contained in the large square.

That is, Area of the large square = (9/100) x 25

                                                      = 9/4 square inches

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.Higher Order Thinking Ari walked 22 miles
at a constant speed of 2 miles per hour. Beth
walked 1 miles at a constant speed of
1 miles per hour. Cindy walked for 1 hour
and 21 minutes at a constant speed of
1 miles per hour. List the three people in order
of the times they spent walking from least time
to greatest time.

Answers

The three people in order of the times they spent walking from least time to greatest time is Beth < Cindy < Ari .

In the question ,

it is given that

Ari walked a distance of 22 miles with speed of 2 miles per hour .

Beth walked a distance of 1 mile with the speed of 1 mile per hour.

Cindy walked for the time 1 hour and 21 minutes .

converting 21 minutes to hours , we get

= 1 hr 21 min

= 1+21/60

= 27/20

= 1.35 hours     ....(i)

time required for Ari to walk 22 miles with speed of 2 miles per hour is

time = distance/speed

time = 22/2 = 11 hours         ...(ii)

time required for Beth to walk 1 miles with speed of 1 miles per hour is

time = 1/1 = 1 hours        ....(iii)

From equation (i) , (ii) and (iii) ,

the order of the time they spent walking from least to greatest time is

1 hours < 1.35 hours < 11 hours

Therefore , the three people in order of the times they spent walking from least time to greatest time is Beth < Cindy < Ari .

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ndiba wants to buy a wagon that costs $217. how much change does he receive if he gives the cashier $250?

Answers

Answer:

change = $33

Step-by-step explanation:

ndiba wants to buy a wagon that costs $217. how much change does he receive if he gives the cashier $250?

250 - 217 = change

change = $33

{assuming no sales tax]

Simplify (-4b)(-19b).
76b
-76b
766²
-76b²

Answers

The answer is the last one. -76b².

Someone please help me with this!!! (Will mark Brainliest)

Answers

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

One of the humpback whales in a pod has a maximum speed of 690 meters per minute. If
the whale is swimming south at one-third of its top speed, how far will the whale travel in
4 minutes?
Write your answer as a whole number.

Answers

690 ÷ 3 = 230

230 × 4 = 960

a whale will go 960 meters

Are 36²y²-25y and 11x²y² equivalent?​

Answers

Answer: No both equations dont have x

Step-by-step explanation:

Identify the vertex, min/max values, and x-
intercepts. Then graph.
y=x²-1

Answers

x-intercepts; plug in 0 for y and then solve

0 = x^2 - 1

1 = x^2; x = -1 & x = 1

vertex; (0,-1); the only translation was the point was moved down one unit

min/max; the graph does not have a max because it is a positive graph w/ positive infinity. The minimum would be (0,-1), the lowest point.

! For graphing I recommend using desmos.

Zak has 11 shirts and 8 ties in his wardrobe. a) On Thursday morning, he picks a shirt and a tie at random from the wardrobe. How many possible combinations are there? b) On Thursday evening, he puts the tie back in the wardrobe but not the shirt. On Friday morning, he picks a shirt and a tie at random from the wardrobe again. How many possible combinations are there now?​

Answers

Answer:

c

Step-by-step explanation:

because you do 12 times 9 minus 100 wich is 125 so yeah

Find a formula for the exponential function passing through the points (-2, 4/9) and (3,108)

Answers

Answer:

[tex]f(x)=4(3)^x[/tex]

Step-by-step explanation:

Let [tex]f(x)=ab^x[/tex].

Then,

[tex]ab^{-2}=\frac{4}{9} \\ \\ ab^3=108 \\ \\ \frac{ab^3}{ab^{-2}}=\frac{108}{4/9} \implies b^5=243 \implies b=3 \\ \\ \therefore a(3)^3=108 \\ \\ a=4 \\ \\ \therefore f(x)=4(3)^x[/tex]

F(x)= 4^3 this is because when following the delta method then plugging it into an equation this would be the answer

Rose's stamp collection is 7 less than half of Van's stamp collection, x.

Which expression represents the total number of stamps that Rose has?

Responses

7−1/2x
7 minus fraction 1 half end fraction x

7x−1/2
7 x minus fraction 1 half end fraction

1/2−7x
fraction 1 half end fraction minus 7 x

1/2x−7

Answers

Answer: 1/2x - 7

Step-by-step explanation:

1/2x represents half of Van's stamp collection and Rose has 7 less than that.

'less than' is telling you to subtract, so the answer is 1/2x - 7

Answer: 1/2x - 7

Step-by-step explanation:

1/2x represents half of Van's stamp collection and Rose has 7 less than that.

'less than' is telling you to subtract, so the answer is 1/2x - 7

yuckyew DID THIS! NOT ME!

Just in need of help please

Answers

The complete details on the table are

Shape:   Length  Height  Area of 1   Number   Total area

Square       12          12          144            1                144

Triangle      12          15          90             4              360

The surface area is 504 square inches

How to determine the surface area?

The square prism represents the given parameter

On the figure, we have the following highlights:

Shape: Square

Number of shapes = 1Base length = 12 inchesHeight = 12 inches

Also, we have

Shape: Triangle

Number of shapes = 4Base length = 12 inchesHeight = 15 inches

This means that

Area of 1 square = Base length * Height

Area of 1 square = 12 inches * 12 inches

Area of 1 square = 144 square inches

So, the area of all squares in the figure is

Area of all squares = 1 * 144 square inches

Area of all squares = 144 square inches

Also, we have

Area of 1 triangle = 0.5 * Base length * Height

Area of 1 triangle = 0.5 * 12 inches * 15 inches

Area of 1 triangle = 90 square inches

So, the area of all triangles in the figure is

Area of all triangles = 4 * 90 square inches

Area of all triangles = 360 square inches

The surface area of the figure is

Surface area = Area of all triangles + Area of all squares

This gives

Surface area = 360 square inches + 144 square inches

Evaluate

Surface area = 504 square inches

Hence, the surface area of the prism is  504 square inches

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The diagonal of a triangle measures 18.2 inches. The width is 6.7 inches. What is the perimeter of the rectangle? (This has to do with Pythagorean Theorem)

Answers

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{18.2}\\ a=\stackrel{adjacent}{6.7}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{18.2^2 - 6.7^2}=b\implies \sqrt{286.35}=b\implies 16.92\approx b[/tex]

-w/5 + nine = thirteen

Answers

Answer:

w=-20

Step-by-step explanation:

-w/5+9=13

-w/5=-1/5w

-1/5w+9=13

Subtract 9 on both side

Multiply both sides by -5/1

w=-20

Answer:

w=20

Step-by-step explanation
.

Write in exponential notation.
(-6)(-6)(-6)(-6) =

Answers

Answer:

[tex] ( - 6) {}^{4} [/tex]

Step-by-step explanation:

-6 is being multiplied repeatedly 4 times so

[tex]( - 6) {}^{4} [/tex]

200-80/1 or (as shown on the sheet)

200-80
------------
1​

Answers

Answer:

120

Step-by-step explanation:

200 - 80 = 120

so 120 / 1 = 120

Answer:

200-80/1 which means (200-80) divided by 1

200 and 80 is in bracket so we solve it first:

200-80=120

now 120/1= 120

Please mark as brainliest

Find the area of the following polygon if AB= 12 cm, AC = 2.4 cm, CE = 6 cm, AD 4.8 cm, CF = GE = 3.6 cm, DH = 2.4 cm. =​

Answers

Answer:

50.40 cm2

Step-by-step explanation:

Area of the polygon AFGBH = Area of ∆ACF + Area of rectangle FCEG + Area of ∆GEB + Area of ∆ABH

= 3.6 cm2 + 4.32 cm2 + 21.6 cm2 + 6.48 cm2 + 14.4 cm2

= 50.40 cm2

Hence, the required area = 50.40 cm2.

Write an equation of a line parallel to y = 2x - 1 that passes through the point (-3, 1)

Answers

The equation of the parallel line to y = 2x - 1, that passes through (-3, 1) is: y = 2x + 7.

How to Write the Equation of Parallel Lines?

Two lines that are parallel to each other would always have the same slope (m). In the slope-intercept form of the equation that represents a line, y = mx + b, the slope of the line is represented as "m", while the y-intercept is represented as b.

Given:

A point (-3, 1)

Equation, y = 2x - 1. The slope (m) = 2. Since parallel lines have the same slope (m), therefore, the line that passes through (-3, 1) also have a slope (m) = 2.

Substitute (x, y) = (-3, 1) and m = 2 into y = mx + b:

1 = 2(-3) + b

1 = -6 + b

1 + 6 = b

b = 7

To write the equation of the parallel line to y = 2x - 1, substitute m = 2 and b = 7 into y = mx + b:

y = 2x + 7.

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If f(x) = 2x² +3 and g(x)=x2-7, find (f- g)(x)


A. 3x²2²-10
B. x² + 10
C. x²-4
D. 3x²2²-4

APEX FUNCTIONS PLEASE HELP​

Answers

Answer: D

Step-by-step explanation:

A transversal interersects two parallel lines. The measures of a pair of alternate interior angles are 5v and 2w. The measures of a pair of same-side exterior angles (consecutive exterior) are 10w and 5v. What are the values of w and v?

Answers

Answer: [tex]v=6, w=15[/tex]

Step-by-step explanation:

The pair of alternate interior angles are congruent, so [tex]5v=2w \implies 10w=25v[/tex].

The consecutive exterior angles are supplementary, so

[tex]10w+5v=180\\\\25v+5v=180\\\\\\30v=180\\\\v=6\\\\\implies w=2.5(6)=15[/tex]

solve g(x) = "-x^2" "-7" when x=-3

Answers

Solution of the given function g(x) = "-x^2" "-7" when x=-3  = 2.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function called g is defined by the notation y=g(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The output value, also known as the dependent variable, is denoted by the letter y, or g(x).

Given function

g(x) = -x² -7When x = -3

Whenever you're given a function, you simply plug in the x  value you're given and then calculate the result.

g(-3) =(-3²) - 7

g(-3) =(9) - 7

g(-3) =9 - 7

g(-3) =2

Hence, When x=-3 = 2, the given function g(x) has a solution of "-x2" "-7."

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9(x+y)=3ay solve for y

Answers

When we solve the linear equation for y, we will get:

8*x/(3*a - 9) = y

That is the solution for the variable y.

How to solve the linear equation for y?

Here we have the linear equation:

9*(x + y) = 3*a*y

Where x, y, and a are variables.

We want to solve this linear equation for y, this means that we need to isolate y in one side of the equation, to do so, let's start by expanding the left side:

9*(x + y) = 3*a*y

9*x + 9*y = 3*a*y

Now we move all the terms with y to the right side.

8x = 3*a*y - 9*y = (3*a - 9)*y

Now we divide both sides by 3*a - 9 to get:

8*x/(3*a - 9) = y

That is the equation solved for y.

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Is 1270.8 cm significantly high?
A. No, because it is below the lower limit separating value.
B. Yes, because it is between the limits separating values.
C. No, because it is above the upper limit separating value.
D. No, because it is between the limits separating values.
E. Yes, because it is above the upper limit separating value.
F. Yes, because it is below the lower limit separating value.

Answers

To determine the boundaries separating numbers that are significantly low or significantly high, apply the range rule of thumb.

How do you identify the limits separating values that are significantly low or significantly high?

To determine the boundaries separating numbers that are significantly low or significantly high, apply the range rule of thumb. Males had pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute, according to Data Set 1 "Body Data" in Appendix B.

A limit exists a specific value to which a function approaches. Estimating a limit usually means finding what value y exists as x approaches a certain number.

Therefore, the correct answer is option A. No, because it is below the lower limit separating value.

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1. Complete the following transactions and explain how they would appear in your register.

• You open your bank account on April 16 with a tax refund check of $145.00.
• You pay SellUPhone $65.34 on April 18. (Check 794)
• You deposit your paycheck on April 23. ($9.76/hour for 35 hours)
• You buy $61.32 (4% sales tax not included) in clothes from BargainsRUs on April 24
using your debit card.

Answers

The following banking transaction completed will appear in the register as follows:

DATE         COMPUTATION                    BALANCE ($)

April 16    145.00                                       145.00

April 18    145.00-65.34=79.66                79.66

April 23   79.66+(9.76)(35)=421.26          421.26

April 24   421.26-(61.32)(1.04)=357.49     357.49

What is a banking transaction?

Any money that transfers into or out of your bank account is considered a bank transaction. Cash withdrawals and deposits, cheques, internet payments, debit card charges, wire transfers, and loan payments are all examples of bank transactions.

In most contexts, the term "register" refers to the process of documenting an event, transaction, name, or other information, or an accumulation of recorded data, often comprising historical events, transactions, names, or other information. Alternatively, the phrase can refer to a record of all debit account charges.

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Find the circumference of a circle with
diameter, d = 7.65m.
Give your answer rounded to 2 DP.

Answers

Answer:

24.03

Step-by-step explanation:

We know  that the formula is pie squared times radius but the radius is half of the diameter but you can also do pie times diameter and get the same answer.

2 In (x - 5) = In (x + 10) + In 4

Answers

answer:

the solution is: x = 15

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