Differentiate the function. f(x) = sin(9 ln(x))

Answers

Answer 1

Answer: [tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex].

Step-by-step explanation:

The given function is

[tex]f(x)=\sin(9\ln (x))[/tex]

Using chain rule differentiate w.r.t. x.

[tex]f'(x)=\cos(9\ln (x))\dfrac{d}{dx}(9\ln (x))[/tex]      [tex]\left[\because \dfrac{d}{dx}\sin x=\cos x\right][/tex]

[tex]f'(x)=\cos(9\ln (x))\left[9\dfrac{d}{dx}(\ln (x))\right][/tex]

[tex]f'(x)=\cos(9\ln (x))\left[9\times \dfrac{1}{x}\right][/tex]       [tex]\left[\because \dfrac{d}{dx}\ln x=\dfrac{1}{x}\right][/tex]

[tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex]

Therefore, [tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex].


Related Questions

A regulation baseball field measures 90 feet between each base. what is the distance around the bases in meters?

Answers

Answer:

27.43 meters in between each base, 109.72 around all the bases.

Step-by-step explanation:

There are 0.3 meters in one foot, so 0.3 x 90= 27.43. 27.43x4=109.72

a principal square root is always...

Answers

Answer:

a principal square root is always positive

Step-by-step explanation:

When you take a square root of a number, you get a positive and negative number

The principal square root is the positive number

True, this is the answer oof

Find the equation of the line with slope 3/5 and y-intercept (0,4)

Answers

Answer:

10,5

Step-by-step explanation:

Answer:

y=3/5x+4

Step-by-step explanation:

slope intercept form is y=mx+b

m=3/5

b=4

Ms. Bailey is taking her children and their friends to the movies. She will pay $10 for her adult ticket and $6 for each child ticket. Ms. Bailey spends $46.00 at the movies. Write and solve an equation to determine the number of child tickets Ms. Bailey purchases.

Please include the Variable, Equation, and the Solution​

Answers

Answer:

Ms. Bailey purchases 6 children tickets

Step-by-step explanation:

x=number of adult tickets

y=number of children tickets

10x+6y=46

plug in what you know

10(1)+6y=46

10+6y=46

subtract 10 from both sides

6y=36

divide both sides by 6

y=6

6 children tickets

Is Nora or Sofia correct? Explain your reasoning.

Answers

Answer:

  Nora is correct

Step-by-step explanation:

Sophia used an appropriate method for computing the value of the repeating decimal fraction ...

  0.1212_12

Close examination of the given decimal fraction shows that it is non-repeating, so is an irrational number. It cannot be represented by the ratio of integers.

Nora is correct in saying Sophia made a mistake.

___

Sophia depended on 100x -x cancelling some part of the fraction, so the result was a finite decimal. For repeating 2-digit fractions, this works well:

  [tex]x=0.12\overline{12}\\100x=12.12\overline{12}\\100x-x=12.12\overline{12}-0.12\overline{12}=12\\x=12/99[/tex]

However, the decimal does not repeat, so this does not work:

  100x = 12.1121112

  100x -x = 12.1121112 -0.121121112 = 11.99099009900099... non-repeating

That is, the decimal part is not cancelled by Sophia's work, as we said above.

5x + y = 12

Solve for y plz

Answers

Answer:

i think 7

Step-by-step explanation:

Answer:

its 7

Step-by-step explanation:

cuz in this you have to move the 5 from the 12 can i have brainleyist

LM is 11x-21 MN is 8x+15

Answers

Answer:

If you are asking me to combine the expressions, then we can combine like terms to get 19x-6

Step-by-step explanation:

The Perez family is researching the cost of keeping their dog at a kennel during an upcoming vacation. The local kennel allows “Silver” families to pay a rate of $36 per day. For a fee, families can buy a “Gold” membership and will be allowed to board their dogs at a discounted rate as shown in the table. Total Cost, Including Membership Fee, to Board a Dog Type of membership 1 Day 2 Days 7 Days Silver $36 $72 $252 Gold $70 $90 $190 What is the cost of a Gold membership? $20 $34 $50 $70

Answers

Answer:

it is 50 dollars

Step-by-step explanation:

Answer:

the answer is c.50

Step-by-step explanation:

i just did the assignment

WHICH DECIMALS ARE REPEATING DECIMALS?
A. 0.375
B. 3.44
C. 4.95

Answers

The answer is B. 3.44

8=3/2(9x-6) and explain

Answers

Exact Form: 34/27

Mixed Number Form: 1 7/27 (one and seven twenty-sevenths)

Decimal Form: 1.259... (never ending)

Isolate the variable by dividing each side by factors that don't contain the variable.

Solve for x (see image)

Answers

Answer:

x = 18

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

x^2 + 24^2 = ( 12+x)^2

FOIL the right side

x^2 +576 = 144 + 24x + x^2

Subtract x^2 from each side

576 = 144 + 24x

Subtract 144 from each side

576-144 = 24x

432 = 24x

Divide each side by 24

432/24 = 24x/24

18=x

Find the unknown angles.​

Answers

Step-by-step explanation:

70°+70°+a°=180°

a°=180°-140°

a°=40°

p°=70° (vertically opposite angle)

q°=70°(alternate interior angles)

hope it helps

Should the painter use stencil one or stencil two for her project? Why? Explain in terms of rigid transformations.

Answers

Answer: The painter should use stencil one for her project because a series of rigid transformations maps stencil one to the original pattern. The shapes are the same because you don’t have to deform stencil one to match the original shape.

Step-by-step explanation:

i just got a 100

I need help with math can someone please help me

Answers

Answer:

133.1

Step-by-step explanation:

Rafael wrote expressions equivalent to 8 using square roots and cube roots. All of the following could be one of Rafael’s expressions except:

Answers

Answer:

it's c

Step-by-step explanation:

Answer:

C.

[tex] \sqrt[3]{64} \times \sqrt[3]{8} [/tex]

A total of 587 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

Answer:

'325 adult tickets' is the ACTUAL answer

Step-by-step explanation:

I am editing this because I made a mistake beforehand

Let's say that x=adult tickets. If we subtract 63 tickets from adult tickets you get the number of children's tickets, so that means x+(x-63)=587. Or,

2x-63=587

Add 63 to both sides to get 2x=650. Divide it all by 2, and you get 325 adult tickets

Solve
y
= x2 + 23 for x.
O A. x= y - 23
O B. = +Jy + 23
O C. X = +VÝ - 23
D. X = y +23

Answers

Answer:

x = ±√(y - 23)

Step-by-step explanation:

y  = x^2 + 23 may be solved for x as follows:

Subtract 23 from both sides, to isolate x^2:

x^2 = y - 23

Take the square root of both sides.   We get:

x = ±√(y - 23)

Hi what’s 2+2? Anyone would like to help..?

Answers

two plus two is four!
you count your fingers

Answer:

2+2 = 4

Step-by-step explanation:

you see..... •• (2) + ••(2) = •••• (4) << you just need to count them

Express the ratio AC/DF in simplest form

Answers

Answer:

[tex] \frac{n}{28 \: cm}[/tex]

Step-by-step explanation:

AC = n, DF = 28 cm

[tex] \huge \red{ \frac{AC}{DF} }= \purple{ \frac{n}{28 \: cm}} \\ [/tex]

5x + 3y = 25 & x - 3y = 15.

Answers

Answer:

x = 20/3

Step-by-step explanation:

What is 16/6 as a decimal?

Answers

To get 16/6 converted to decimal, you simply divide 16 by 6.

(-1/3)-(-9/5) to the lowest term

Answers

Answer:

Step-by-step explanation:

-1/3 + 9/5

-3/15 + 27/15

24/15 = 8/5 = 1 3/5

On January 1, 2009, Jessica owed $10,212 to her friend Sam, who was kind enough not to charge Jessica any interest. Each month during 2009, Jessica paid Sam some of the money she owed. If Jessica still owed Sam $6,612 on January 1, 2010, what was the average amount of Jessica's monthly payments?

Answers

Answer:

551

Step-by-step explanation:

6612 divided by 12 ( number of months) =551

Donovan wants to earn a 70% in Mr. Mottola's class. He knows he currently has an 67% in the class after 9 grades. What is the minimum grade Donovan would need to earn in order to have a 70%.

Answers

Donovan needs to earn at least a 73% in order to have a 70%

is -4 greater or lesser than 0

Answers

Answer:

-4 is lesser than 0

Step-by-step explanation:

write two and six hundreds nineteen thousandths in decimal.​

Answers

Answer:

Easy .2619

Step-by-step explanation:

hope it helped

I got “.2619” as the answer

A school installs a ramp that will rest on a landing 2 feet high. The ramp is 24 feet long. According to building code, the ramp must not be greater than a 5° angle with the ground. What is the angle formed from the ground? Is the school in compliance with the building code? Group of answer choices

85degree; no


3degree; yes


5degree; yes


8degree; no

Answers

Hey there! I'm happy to help!

Our angle is facing the 2 foot high landing. This is the opposite side of the angle. We also have the ramp, which is the hypotenuse. The sine is the opposite over the hypotenuse. Since we have these two, we find the [tex]sin^-^1[/tex] to give the the angle.

[tex]sin^-^1(2/24)=4.780191847....[/tex]

This angle is about 5 degrees and it is in compliance with the building code because it is not greater than 5 degrees.

Have a wonderful day! :D

what is 2*2 please answer this question

Answers

Answer:

4

Step-by-step explanation:

Answer:

5-1

Step-by-step explanation:

9. What is the angle of rotation for the following figure?
HELP
HELPPP

Answers

Answer:

90° im pretty sure is the correct answer

90 is the correct I’m pretty sure

What are the possible values for p
Ipl = 12

Answers

Answer:

Step-by-step explanation:

|p|=12

p=±12

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