what is the value of d/dx(1/x) at x=6 ?​

Answers

Answer 1

If you know your derivative rules, then

d/dx [1/x] = -1/x ²

so that when x = 6, the derivative has a value of -1/36.

If you have to use the definition of the derivative, then

d/dx [1/x] = lim {h → 0} (1/(x + h) - 1/x) / h

… = lim {h → 0} (x - (x + h)) / (hx (x + h))

… = lim {h → 0} (-h) / (hx (x + h))

… = lim {h → 0} (-1) / (x (x + h))

… = -1/x ²

and at x = 6, you again get -1/36.

Alternatively, use the definition of the derivative at a point:

d/dx [1/x] (6) = lim {x → 6} (1/x - 1/6) / (x - 6)

… = lim {x → 6} ((6 - x) / (6x)) / (x - 6)

… = lim {x → 6} -(x - 6) / (6x (x - 6))

… = lim {x → 6} (-1) / (6x)

… = -1/36


Related Questions

Determine the AMPLITUDE and the MIDLINE of the sine function below.*
1 poin
y = – 3sin(2x) - 5
a. Amplitude = -3, Midline = -5
b. Amplitude = 3, Midline 5
c. Amplitude = 3, Midline - 5
d. Amplitude = 2, Midline = – 3
O a.

Answers

Step-by-step explanation:

Amplitude of the sine function is 1.

So if its multiplied by -3, its amplitude is 3 (its always positive).

The midline of sin x is 0.

The midline of sin 2x is also 0.

The midline of -3*sin 2x is also 0.

So if you subtract this function by 5, then the new midline is -5.

The Rodriguez
family is on a
vacation. They
started with $1,875.
They have spent
$140 each day and
have $895 left for the
rest of their vacation.
Write and solve an
equation to find how
many days have they
been on their
vacation already?

Answers

1,875 - 895 = 980 dollars they spent. 980 divided by 140 equals 7. They have been on their vacation for 7 days.

Write the missing decimal so that each pair adds to 1/2 + ...= 1

Answers

Answer:

0.5

Step-by-step explanation:

1/2 + 0.5 = 1

20.) Using the cross multiplication method, which of the following is the solution to 18/6x = 4/(x+3)?


a)9


b)-9


c)12


d)-12

Answers

Answer:

B. 9

Step-by-step explanation:

Which conic section is represented by the following equation? 9x^2 – 5x – 3y^2 – 2y + 4 = 0

Answers

Answer:

D. Hyperbola

Step-by-step explanation:

I put B but it was wrong

D is the right answer

The given equation is represent a ''Hyperbola''.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ 9x² - 5x - 3y² - 2y + 4 = 0

Now, We know that;

The standard form of the equation is,

⇒ ax² + by² + 2gx + 2fy + 2hxy + c = 0

For Hyperbola, The condition is,

⇒ h² > ab

For Ellipse ,  The condition is,

⇒ h² < ab

Here, We have;

⇒ h = 0

⇒ a = 9

⇒ b = - 3

⇒ ab = 9 x - 3 = - 27

⇒ h = 0

Hence, We get;

⇒ 0 > - 27

⇒ h² > ab

Thus, This equation is represent a ''Hyperbola''.

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Point A is located at (4,0) and is reflected in the x-axis. What are the coordinates of point A'?
O (0,4)
0 (0,-4)
O 1-4,0)
O (4,0)

Answers

Answer:

(4,0)

Step-by-step explanation:

-8h+z/7
Use z=21 and h=4

Answers

Answer:

Hope this helps

Step-by-step explanation:

Question 3: Add 9 to 5 times n to get 3 is reprented as​

Answers

Answer:

5n + 9 = 3

I hope im right!!

5n + 9 = 3

because it says add 9 , then you do 5xn which is 5n & you would get 3

how many millimeters are in 7 liters​

Answers

7 liter = 7000000 cubic millimeters

7000000 cubic millimeters

A salt mixture has 8 parts water and 2 parts salt. Suppose one part of each is added. What is the new ratio of salt to
water?
O 2 to 9
O 3 to 8
03 to 9
O. 9 to 3

Answers

0.9 to 3 is the answer

Answer:

3 to 9 I guess...................

Simplify 9р – 2р +р

Answers

Answer:

8P

Step-by-step explanation:

Answer:

8p

Step-by-step explanation:

9р – 2р +р

7p+p

8p

What is the slope of the line that passes through (0, -4) and (6,4)? *
3/4
4/3
0 -3/4
- 4/3

Answers

ANSWER:

The Slope to your answer is 4/3

Instead I’d using the values 1,2,3,4,5,6 on dice, suppose a pair of dice have the following 1,2,2,3,3,4 on one die and 1,3,4,5,6.8 on the other.find the probability of rolling a sum of 12

Answers

Answer:1/24

Step-by-step explanation:

Since the first die has 4 distinct numbers, and second has 6 distinct numbers, so total number of combinations possible = 4 × 6 = 24

Now, the number of chances where we get the rolling sum as 12 is only one. (

Therefore, the probability of getting sum 12 is 1/24

Answer:

1/36

Step-by-step explanation:

For the acellus people

What is one method to find the measure of angle B?
A. use the Pythagorean theorem to find BC, then solve the equation tan(B)=8/BC
B. because of the 30-60-90 triangle theorem, you know the measure of angle B is 60
C. solve the equation cos(B)=8/89(square rooted)

The answer is A

Answers

Answer:

A

Step-by-step explanation:

edg2021

One method to find angle B is A. use the Pythagorean theorem to find BC, then solve the equation tan(B)=8/BC.

What is Pythagoras Theorem?

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a right angled triangle ABC with the hypotenuse being AB and the legs AC is the base and BC is the height.

Given AC = 8 and AB = √89.

We need to find the measure for angle B.

Either we can find angle B using Sin B = Opposite side / hypotenuse

Sin B = 8 / √89

But this is not in the option.

So first find the length of BC using the Pythagoras Theorem.

(BC)² = (AB)² - (AC)²

         = (√89)² - (8)²

         = 25

BC = √25 = 5

We get the opposite side and adjacent side with respect to angle B.

Tan B = AC / BC = 8 / 5 = 1.6

B = 57.99° ≈ 58°

Hence the approximate measure of angle B is 58°.

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Complete the table for y=1/5x+1 and graph the resulting line

Answers

Sorry this is really sloppy but hope this helps!

Answer:

x=-5 y=0

x=0 y=1

x=5 y=2

x=10 y=3

Which equation can be used to find the volume of the cylinder?

A cylinder with a radius of 6 centimeters and a height of 8 centimeters.


V = pi (6) squared (8)
V = pi (12) squared (8)
V = pi (8) squared (6)
V = pi (8) squared (8)

Answers

V = pi (6) squared (8)

Explanation: The formula for finding the volume of a cylinder is V = pi (radius) squared (height) so you just fill in the numbers and boom

Answer:

I think it's A. V = pi (6) squared (8)

(I'm so sorry if it's wrong)

Hope this Helps!

caroline can sketch 5 cartoon strips in two hours. How long will it take her to sketch 20 strips

Answers

Answer:

8 hours

Step-by-step explanation:

20÷5 = 4

4×2 = 8

Hope this Helps!

:)

Find the surface area of the cylinder: Use 3.14 for
2 cm
15 cm
A. 100.48 cm
B. 97,43 cm
C. 36.28 cm
D. 33.14 cm
2 of 4 Answered

Answers

Answer:

Well on my end i got 47.12, with pi included

Step-by-step explanation:

The surface area of the cylinder with the diameter 2cm and height 15cm  is [tex]100.48 \; cm^2[/tex]

Calculation to find Surface area of cylinder:

Given the diameter of the cylinder is 2cm and height  15cm

Formula :

The surface area of the cylinder =[tex]2\pi r^2+2\pi rh[/tex]

where 'r' is the radius and 'h' is the height of the cylinder

Diameter = 2cm

[tex]radius =\frac{diameter }{2} =\frac{2}{2} =1[/tex]

radius = 1cm and height is 15 cm

the value of pi is 3.14

Substiute all the values

[tex]SA = 2\pi r^2+2\pi rh\\SA=2(3.14)(1)^2+2(3.14)(1)(15)\\SA=6.28+94.2\\SA=100.48 cm^2[/tex]

The surface area of the cylinder with the diameter 2cm and height 15cm  is [tex]100.48 \; cm^2[/tex]

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What is the range of y=the squareroot of x+7+5

Answers

The range of the function is the set of all positive real numbers, or y > 0.

What is the range of a function?

The range of a function is the set of all possible values that the function can output.

The function is given in the question as:

y = √(x+7+5)

In the case of the function y = √x + 7 + 5, the range is the set of all possible values of y that can be obtained by substituting different values of x into the function.

To find the range of this function, we need to consider the values of x that can be used in the function. The square root of a number must be non-negative, so x must be greater than or equal to 0.

In other words, the domain of the function is x ≥ 0.

We can now substitute different values of x into the function to find the range.

For example, if x = 0, then y = √0 + 7 + 5 = 7 + 5 = 12. If x = 1, then y = √1 + 7 + 5 = 8 + 5 = 13. And so on.

We can see that as we increase the value of x, the value of y also increases. This means that the range of the function is the set of all positive real numbers, or y > 0.

Therefore, the range of y = √x + 7 + 5 is y > 0.

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Answer:  b - edge

Step-by-step explanation:

Simplify each of the fractions. If there is no answer, enter "undefined."
C. 16/0

Answers

1 whole???i’m not smart lol

Do you like penguins? btw does 1-5=3​

Answers

Answer:

I like looking and drawing a penguins

Step-by-step explanation:

And no 1-5 is not 3, it is -4

I need help with this geometry question

Answers

Answer:

24

Step-by-step explanation:

2 log x + log 11
WILL MARK BRAINLIEST

Answers

Answer:

[tex] log(11 {x}^{2} )[/tex]

Step-by-step explanation:

[tex]2logx + log11 \\ \\ = log {x}^{2} + log11 \\ \\ = log( {x}^{2} \times 11) \\ \\ = log(11 {x}^{2} )[/tex]

The Equivalent value of 2 log x + log 11 is log(11x²).

What is Logarithm?

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be represented as multiplication and division of logarithms.

We have to find the value of 2 log x + log 11.

Using the property

log a + log b = log (ab)

and, 2 log a = log a²

So, 2 log x + log 11

= log x² + log 11

= log( x² × 11)

= log(11x²)

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There are 204 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 42 fans?

Answers

Answer:

there will be 5 busses or 4.8 needed

In Sally's grade, there are 60 students. Currently, 10% of them are enrolled in health. How
many students are enrolled in health?

Answers

Answer:

6 Students

Step-by-step explanation:

10% of 60 is 6.

6 students I think 60-90%

Fire works are fired vertically upwards from a platform 10 feet above the ground and with an initial velocity of 96 feet per second what is the highest possible point for the fireworks to explode

Answers

Answer:

Here is the answer

Step-by-step explanation:

The highest possible point for the fireworks to explode is to be considered as the 154 feet.

Calculation of the highest possible point:

Since the equation is

[tex]h = -16t^2 + 96t 10[/tex]

Now based on this, we have to determine the axis of symmetry

So,

[tex]t = -b \div 2a\\\\= -96 \div 32[/tex]

= 3

Now

[tex]= -16(3)^2 + 96(3) + 10[/tex]

= 154 feet

hence, The highest possible point for the fireworks to explode is to be considered as the 154 feet.

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URGENT HELP!!! PLEASE!!!

Answers

green 1 red 5 black -2 blue 1
Green 1 red 5 black -2 blue 1

Which number is between 0.4 and 0.5?
A 0.04

0.44
0.05
0.50

Answers

.44 is the correct answer

suppose you deposit $1000 in a savings account that pays 4.8% interest compounded monthly. Write an exponential function to model the amount of money in your savings account. How much will you have in your account after 2 years?

Answers

Answer:

The exponential function is [tex]A(t) = 1000(1.004)^{12t}[/tex].

You will have $1,100.55 in the account after 2 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Deposit $1000 in a savings account that pays 4.8% interest compounded monthly.

This means that [tex]P = 1000, r = 0.048, n = 12[/tex]. So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 1000(1 + \frac{0.048}{12})^{12t}[/tex]

[tex]A(t) = 1000(1 + 0.004)^{12t}[/tex]

[tex]A(t) = 1000(1.004)^{12t}[/tex]

This is the exponential function

How much will you have in your account after 2 years?

This is A(2). So

[tex]A(2) = 1000(1.004)^{24} = 1100.55[/tex]

You will have $1,100.55 in the account after 2 years.

What is the slope of this graph? I WILL GIVE BRAINLIEST PLSSSS 100 points 3,2 1,4

Answers

Step-by-step explanation:

Slope = -5/5 = -1

Answer:

m=-1

Step-by-step explanation:

Slope is equal to the change in

y, over the change in x, (or rise over run)

pick any two points on the line to apply to this formula.

m= 3-(2) / 2-(3)

m=-1

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