Derivative of (x^7+2x-3)^3

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{dy}{dx} = 3(7x^6 + 2)(x^7 + 2x - 3)^2[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = (x^7 + 2x - 3)^3[/tex]

Step 2: Differentiate

Basic Power Rule [Derivative Rule - Chain Rule]:                                       [tex]\displaystyle y' = 3(x^7 + 2x - 3)^2(x^7 + 2x - 3)'[/tex]Basic Power Rule [Derivative Properties]:                                                   [tex]\displaystyle y' = 3(7x^6 + 2)(x^7 + 2x - 3)^2[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation


Related Questions

A circle has a diameter of 18 feet. Which following is closest to the l circumference of the circle?
A-28.3ft
B-56.5ft
C-113.1ft
D-245.5ft​

Answers

circumference =2×pi×r

18/2=9(r)

so...2×pi×9

=54..5

Answer:

56.5 ft

Step-by-step explanation:

We define the number π as the ratio between the circumference and diameter of a circle: π = c/d. Rearranging this equation gives us one for the circumference: c = πd. Using an approximation of π ≈ 3.14 and our value of d = 18 feet, we can find that c = 3.14(18) = 56.52 ft, or 56.5 ft, rounded to the nearest tenth.

Simplify: −2[−3(x − 2y) + 4y].
thanks!

Answers

Answer:

6x − 20y

Step-by-step explanation:

−2[−3(x − 2y) + 4y] =

= −2[−3x + 6y + 4y]

= −2[−3x + 10y]

= 6x − 20y

Answer:

Step-by-step explanation:

Here you go mate

PEDMAS:

Parenthesis

Exponent

Multiplication

Addition

Subtraction

Step 1

−2[−3(x − 2y) + 4y]  Equation

Step 2

-2[-3(x -2y) + 4y]  simplify

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

Step 3

(-2)(-3(x-2y))+(-2)(4y)   Add,Subtract And Remove parenthesis

6x-12y-8y

answer

6x-20y

According to a recent survey of adults, 38% say the almond is their favorite nut. The adults were also asked where they lived. Of the 19% of those who responded that they live in California, 40% chose the almond as their favorite nut.


Is liking almonds independent of residency?


Yes, P(almonds) = P(California|almonds).

Yes, P(almonds) = P(almonds|California).

No, P(almonds) ≠ P(California|almonds).

No, P(almond) ≠ P(almonds|California).

Answers

Answer:

No, P(almond) ≠ P(almonds|California).

Step-by-step explanation:

In this question, we have that:

38% of adults say that almond is their favorite nut.

Of those adults surveyed, 19% live in California, and of those, 40% chose the almond as their favorite nut.

Since the probabilities are not equal(probability of liking almonds and probability of liking almonds, given that the person lives in California), we have that liking almonds is not independent of residency, and the correct option is:

No, P(almond) ≠ P(almonds|California).

No, P(almond) ≠ P(almonds| Is liking almonds independent of residency.

Given that,

According to a recent survey of adults, 38% say the almond is their favorite nut.

The adults were also asked where they lived.

Of the 19% of those who responded that they live in California, 40% chose the almond as their favorite nut.

We have to determine,

Is liking almonds independent of residency.

According to the question,

38% say the almond is their favorite nut.

The adults were also asked where they lived.

Of the 19% of those who responded that they live in California, 40% chose the almond as their favorite nut.

An independent event and probability, the outcomes in an experiment are termed as events. Ideally, there are multiple events like mutually exclusive events, independent events, dependent events, and more.

Since the probabilities are not equal(probability of liking almonds and probability of liking almonds, given that the person lives in California), we have that liking almond is not independent of residency.

Hence, No, P(almond) ≠ P(almonds| Is liking almonds independent of residency.

To know more about Probability click the link given below.

https://brainly.com/question/23044118

Which sequence is ARITHMETIC?
A)
{0, 1,4,9,...}
B)
{0, 4, 7, 11,...}
{-3, 2, 7, 12,...}
D)
{2, 1, 0.5, 0.25, ...)

Answers

Answer:

c

Step-by-step explanation:

2-(-3)= 5

so the common difference is 5

C

It adds five every time

please can i have a good answer please

Answers

Answer: i could be worng but i will try to answer it nicely and i don´t known how to explaine so i will only tell answer ok? if yes thx.If no than i am sorry

Step-by-step explanation: 162 .will be the answer if it is worng i am so         sorry     :(

2 tickets are $36. we can simplify this to figure out what 1 ticket costs.

36/2 = 18. so 1 ticket costs $18.

9 x 18 = 162.

so, 9 tickets cost $162

What is the mode of the data set?
8 5 3 9 12 9 2 3 6 11

Answers

Answer:

either 3 or 9

Step-by-step explanation:

3 and 9 repeat the most

Julio can stock an aisle at the grocery store in 5 hours. Janet can stock the same aisle in 3 hours. How long will it take
them to stock the aisle if they work together?

Answers

Answer:

2

Step-by-step explanation:

5-3=2

#5-9: Match each equation with the description of its graph below.(Plz answer! I really NEED help!!!!)

Answers

Answer:

[tex]5)y = \frac{7}{8}x + 1 \\ 6)y = - 10x \\ 7)y = 2.5x - 7 \\ 8)y = 1.2x \\ 9)y = - 5x - 8[/tex]

An expression is shown below.
(x4/3)(x2/3)
What is the product of the two factors?

Answers

Answer- hsbshsianao
Step by step
By the first law of exponents (an Algebra 1 concept)

(x4/3)(x2/3) = x4/3 + 2/3

What is the slope of the line that passes through the points (1,1) and (-1,5)

Answers

(1,1)(-1,5)

your answer would be m=-2

hope this helped.

True or False?

The following relation represent a function.

Question 4 options:
True
False

Answers

I think it’s true. If I’m right give me brainiest plz!
Where is the problem?

Jack and Jill fetched 24 pints of water in their bucket. Jill drank a tenth of this, jack a quarter. They gave three eighths to dame Dob and a fifth to jill's mother.

Answers

Answer: See explanation

Step-by-step explanation:

Total water fetched = 24 pints.

Jill drank a tenth of this. This will be:

= 1/10 × 24

= 2.4 pints

Jack drank a quarter. This will be:

= 1/4 × 24 = 6.

They gave three eighths to dame Dob . Thus will be:

= 3/8 × 24

= 9

They gave a fifth to jill's mother. This will be:

= 1/5 × 24.

= 4.80

Amount that'll be left over will be:

= 24 - (2.40 + 6 + 9 + 4.80)

= 24 - 22.2

= 1.8

1.8 pints of water will be left over.

What is the result of adding these two equations?
- 2x + y = -5
- 2x - 4y = 6

Answers

Answer: 5y = -11

Step-by-step explanation:

-2x + y = -5

(-2x - 4y = 6) -1

-2x + y = -5

2x + 4y = -6

System by elimination method

0 + 5y = -11

5y = -11

Answer:

-4x-3y=1

Step-by-step explanation:

when adding the wo equations, u must add like ters. -2x+-2x is -4x. and positive y+ -y= -3y and-5+6=1. so if u put it all together after adding all integers you get -4x-3y=1

If Steph Curry can shoot 72 free throws in 12 minutes, how many free throws
would he shoot each minute?

Answers

Answer:

6

Step-by-step explanation:

72/12=6 shoots each minute

Answer:

The answer is 6

Step-by-step explanation:

72 divided by 12 = 6

Which describes the inequality y > -15?

Answers

Answer:

A

Step-by-step explanation:

                        .

A line passes through the points (4,20) and (8,24) Write a linear function rule in terms of x and y for this line. The linear function rule is y=

Answers

Answer:

so m=2 so y=2x+-3

Step-by-step explanation:

The linear function rule is y = x + 16

What is a Linear equation?

A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, A line passes through the points (4,20) and (8,24)

From the slope-intercept form of a line:

Y = mx + c

Where,

m = slope = (y₂ - y₁)/ (x₂ - x₁)

c = constant

In our case,

m = (24 -20)/ 8-4

m = 4/4

m = 1

So the equation of a line

y = x + c

Since, this line passes through the point(4, 20)

20 = 4 + c

c = 16

Therefore, the equation of the line passes through the points (4,20) and (8,24) is y = x + 16

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ2

Silas had 3 times as much money as Raja. Silas spent $84 of his money to buy a birthday gift for his grandma while Raja was awarded $42 for winning a competition. In the end, they had the same amount of money. How much did they have altogether at first?

Answers

Answer:

Total amount Silas and Raja has at first = $252

Step-by-step explanation:

Let,

Amount Silas had = x

Amount Raja had = y

According to given statement;

x = 3y       Eqn 1

x-84 = y+42     Eqn 2

Putting value of x from Eqn 1 in Eqn 2

3y - 84 = y+42

3y-y = 42+84

2y = 126

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{126}{2}\\y=63[/tex]

Putting y = 63 in Eqn 1

x = 63(3)

x = 189

Total amount they had = 189 + 63 = $252

Hence,

Total amount Silas and Raja has at first = $252

The amount they have altogether at first is $252

Let

Raja money = x

Silas had 3 times as much money as Raja. Therefore, Silas money is as follows:

3x

Silas spent $84 of his money to buy a birthday gift for his grandma. Therefore, he has the following amount:

3x - 84

Raja was awarded $42 for winning a competition. Therefore, Raja amount is as follows;

x + 42

In the end, they had the same amount of money. Therefore,

3x - 84 = x + 42

3x - 84 = x + 42

3x - x = 42 + 84

2x = 126

x = 126 / 2

x = 63

Total amount(at first):x + 3x = 63 + 3(63) = $252

learn more on equation here: https://brainly.com/question/228711?referrer=searchResults

Who can help on this for brainliest ?

Answers

Answer:

6

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex]÷[tex]\frac{1}{4}[/tex]=

[tex]\frac{3}{2} *\frac{4}{1}[/tex]=

6

Hope this helps!

Pls give brainliest

Answer:

3 or 6

Step-by-step explanation:

im pretty sure its 3 or 6

Index notation of 5 x 5 x 5 x 5​

Answers

5^4 (five to the 4th power)

Answer:

5^4

Step-by-step explanation:

The pyramid has a base that is a right
triangle with side lengths 3 feet , 4 feef , 5 feet .it’s height is 6 feet. What is the volume of the pyramid?

Answers

Answer:

36

OR

12

?

Step-by-step explanation:

Area of Triangle:   [tex]\frac{3*4}{2} = 6[/tex]

Volume:   6*6 = 36

Pyramid part confuses me.

volume of a pyramid:   [tex]\frac{1}{3}*B*H[/tex] = [tex]\frac{1}{3}*6*6[/tex] = 12

B = triangle area

H = height

Solve the following system of equations using substitution or elimination: y = −8x − 9 y = −6x + 5

Answers

Answer:

x = -7

y = 47

Step-by-step explanation:

Given the system of equation

y = −8x − 9 ... 1

y = −6x + 5 ...2

Equating both expressions

-8x - 9 = -6x + 5

Collect like terms

-8x + 6x = 5 + 9

-2x = 14

x = 14/-2

x = -7

Substitute x = -7 into equation 1.

From 1: y = −8x − 9

y = -8(-7) - 9

y = 56 - 9

y = 47

Hence the solution to the system of equations (x, y) is (-7, 47)

Use A(-1, -2) and B(8,0) to find the length of AB. Round your answer
to the nearest hundredth.

Answers

9514 1404 393

Answer:

  9.22

Step-by-step explanation:

The distance formula is ...

  d = √((x2 -x1)^2 +(y2 -y1)^2)

Using the given coordinates, the distance between them is ...

  d = √((8-(-1))^2 +(0 -(-2))^2) = √(9^2 +2^2) = √85 ≈ 9.22

The length of AB is about 9.22 units.

Which correlation coefficient represents a weak, positive linear relationship?

Select one:
a. r = 0
b. r = 0.35
c. r = −0.35
d. r = 0.94
e. r = −0.94

Answers

Step-by-step explanation:

The Correlation Coefficient

When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation of -0.97 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation.

pls help asap !!!!!!

Answers

Answer:

could you try 33?

Step-by-step explanation:

if Rs is half that could be qt and z is the other 33.

Can someone please help me!!

Answers

Answer:

We conclude that the price per pound of the grapes = $1.45

Hence, option A is true.

Step-by-step explanation:

Given the table

Pounds of Grapes         Total Cost

1.2                                    $1.74

2.6                                   $3.77

4.4                                    $6.38

Total pounds of Grapes = 1.2+2.6+4.4

                                               = 8.2 pounds

Aggregate cost = 1.74 + 3.77 + 6.38

                                  = $11.89

Thus,

Prince per pound = Aggregate cost / Total pounds of Grapes

                              = 11.89  / 8.2

                              = $1.45

Therefore, we conclude that the price per pound of the grapes = $1.45

Hence, option A is true.

If 2.29 x 19.79 = 45.3191, then without actual multiplication the value of 0.0229 x 1979 is?
If you answer this first, I will give brainliest.

Answers

Answer:

45.3191

Step-by-step explanation:

0.0229 is 100 times smaller that 2.29 but 1979 is 100 times greater than 19.79. Since they cancel each other out, the answer remains the same.

39.) A shirt that costs $30 is on sale for 20% off. What is the total cost of the
shirt?

Answers

Answer:

24$

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

The running time (in minutes) of a TV episode is 60-2c where c is the number of commericals aired during the episode. What is the running time of an episode with 15 commercials?

Answers

Answer:

60-2(15)=?

60-30=30

30 minutes

PLESE HELP I WILL GIVE BRAINLEST WORTH 18 POINTS ANSWER IF YOU ARE 100% SURE GIVE EXPLINATION

A flower bed is in the shape of a triangle, with a base of 13 feet and a height of 5 feet. What is the area of the flower bed?

1. 18 square feet

2. 32.5 square feet

3. 65 square feet

4. 130.5 square feet

Answers

Answer:

32.5

Step-by-step explanation:

For triangles you need to do base times height divided by 2

Answer:

Number 2: 32.5 square feet

Step-by-step explanation:

The formula for the area of a triangle is 1/2(base)(height)

In this case, our base is 13 ft and our height is 5 ft so we plug in those values into our formula

A = 1/2(13)(5) = 32.5

Therefore our area is 32.5 square feet.

who ever anwser my question fast and is quick i will give any body 200 point i will any one

Answers

Answer:

omg, can i have freeee points?? :,)

Step-by-step explanation:

Answer: Sure, but I want to be the brainiest for extra points :)

Step-by-step explanation:

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