Use logarithmic differentiation to find the derivative with respect to x of the function y= (sin x)^lnx

Answers

Answer 1
logarithmic differentiation means tAke logarithm of both sides to make the function easier to find the derivative.

y = (sinx)^lnx

ln(y) = ln((sinx)^lnx)

power rule logarithm

ln(y) = ln(x) ln(sinx)

Take derivative

y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx

multiply both sides by y

y' = y( ln(sinx)/x + ln(x)cotx )

remember y = (sinx)^lnx
sub this in for y

y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx

Related Questions

Which of the following is not acceptable form of proof

Answers

What are the options following?

Is this answer correct? If not what is the correct answer

Answers

Hello,

Let 's assume AD=x,DC=6-x.
Using angle nisector theorem:
AD/DC=AB/AC
==> x/(6-x)=8/10
==>10x=48-8x
==>18x=48
==>x=48/18
==>x=24/9=2+2/3 (2.666666666.....)
Answer is false,  the correct answer is 2 2/3

Answer:

no

Step-by-step explanation:

A bread company makes 9 types of bread. A restaurant chain ordered 497 loaves of each kind of bread. How many loaves of bread in total did the restaurant chain order?

Answers

9 types of bread....a restaurant orders 497 loaves of each type

so there are (497 * 9) = 4473 loaves ordered in total

Find the value of the variable and YZ if Y is between X and Z. XY= 11, YZ=4c, XZ=83

Answers

Answer:  The required value of the variable c is 18 and that of YZ is 72.

Step-by-step explanation:  Given that Y is in between X and Z, where

XY= 11, YZ=4c and XZ=83.

We are to find the value of the variable c and YZ.

Since the point Y is in between X and Z, so we must have

[tex]XY+YZ=XZ\\\\\Rightarrow 11+4c=83\\\\\Rightarrow 4c=83-11\\\\\Rightarrow 4c=72\\\\\Rightarrow c=\dfrac{72}{4}\\\\\Rightarrow c=18.[/tex]

And,

[tex]YZ=4c=4\times 18=72.[/tex]

Thus, the required value of the variable c is 18 and that of YZ is 72.

Final answer:

The given problem is a segment addition problem in geometry. It can be solved by creating an equation based on the Segment Addition Postulate, simplifying and solving it to find the value of the variable c equal to 18. Substituting this value into the equation for YZ gives a result of 72.

Explanation:

The subject of this question is a segment addition problem in geometry. From the given values, we can create an equation based on the Segment Addition Postulate, which states that the length of the whole line segment (XZ in this case) is equal to the sum of the lengths of the two segments it is split into (XY and YZ in this context).

With XZ = 83, XY = 11, and YZ = 4c, the equation becomes XY + YZ = XZ, or 11 + 4c = 83. To solve for the value of the variable c, subtract 11 from both sides, giving 4c = 72. Finally, divide each side by 4 to find that c = 18.

To find the value of YZ, substitute c = 18 back into the YZ equation: YZ = 4c = 4*18 = 72.

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neil has 3 partially full cans of white paint. they contain 1/3 gallon 1/5 gallon and 1/2 gallon of paint. about how much paint does neil have in all

Answers

Final answer:

Neil has approximately 21/30 gallon of paint in total.

Explanation:

To find out how much paint Neil has in total, we need to add up the amounts of paint in each can.

The first can contains 1/3 gallon of paint, the second can contains 1/5 gallon of paint, and the third can contains 1/2 gallon of paint.

To add fractions, we need to find a common denominator. In this case, the common denominator is 30. We can convert the fractions to have a denominator of 30 and then add the numerators:

1/3 gallon + 6/30 gallon + 15/30 gallon = 21/30 gallon.

Therefore, Neil has approximately 21/30 gallon of paint in total.

Final answer:

Neil has a total of 31/30 gallons of white paint when his three cans containing 1/3, 1/5, and 1/2 gallon are added together, which is slightly more than 1 gallon.

Explanation:

Neil has three partially full cans of white paint with quantities of 1/3 gallon, 1/5 gallon, and 1/2 gallon. To find the total amount of white paint Neil has, we simply need to add these fractions together. Adding fractions involves finding a common denominator and then adding the numerators.

In this case, the common denominator for 3, 5, and 2 would be 30, so the fractions would be equivalent to 10/30, 6/30, and 15/30, respectively. Now, we add the numerators:

10/30 + 6/30 + 15/30 = 31/30 gallons

So Neil has 31/30 gallons of white paint in total, which is a little more than 1 gallon when converted from an improper fraction to a mixed number (1 gallon and 1/30 of a gallon).

You have 12 product displays. Six have 4 shelves and six have 3 shelves. It is store policy to dedicate at least one full shelf to each product. What is the maximum number of products you can have?

Answers

The answer to this question is 42

Answer: There are 42 products he can have at maximum.

Step-by-step explanation:

Since we have given that

Number of products displays = 12

Number of shelves six products have = 4

Number of shelves six products have = 3

So, total number of shelves first six products have

[tex]6\times 4=24[/tex]

Total number of shelves next six products have

[tex]6\times 3\\\\=18[/tex]

So, the maximum number of products that he can have is given by

[tex]24+18=42[/tex]

Hence, there are 42 products he can have at maximum.

Nicole bought a new TV at Target for $384.87. if the TV was on sale for 25% off and she paid with her red card which earned her another 5% off , and the tax rate is 8.25% what was the original price of the TV ? Be sure to show how you arrived at your answer

Answers

Let x = the original price.

With 25% off, the price drops to
0.75x.
With another 5% off, the price drops to
0.95*(0.75x) = 0.7125x
Add 8.25% tax, and the price goes up to
1.0825*(0.7125x) = 0.7713x

This is equal to the amount paid, so
0.7713x = 384.87
x = 384.87/0.7713 = $498.99

Answer: Original price = $498.99

How Do I Solve Question 8 ?

Answers

8)

[tex]\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(x,y)\qquad C(12,5)\qquad \qquad AB:BC\qquad 3:4\to \frac{3}{4} \\\\\\ \cfrac{AB}{BC} = \cfrac{3}{4}\implies \cfrac{A}{C}=\cfrac{3}{4}\implies 4A=3C\implies 4(x,y)=3(12,5) \\\\\\ -------------------------------\\\\ { B=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}\\\\ -------------------------------\\\\[/tex]

[tex]\bf B=\left(\cfrac{(4\cdot x)+(3\cdot 12)}{3+4}\quad ,\quad \cfrac{(4\cdot y)+(3\cdot 5)}{3+4}\right)=\stackrel{B}{(4,1)} \\\\\\ \left(\cfrac{4x+36}{7}~,~\cfrac{4y+15}{7} \right)=(4,1)\implies \begin{cases} \cfrac{4x+36}{7}=4\\\\ 4x+36=28\\ 4x=-8\\ \boxed{x=-2}\\ ----------\\ \cfrac{4y+15}{7}=1\\\\ 4y+15=7\\ 4y=-8\\ \boxed{y=-2} \end{cases}[/tex]

If it is 10:00 am at your location when it is noon along the prime meridian, what is your longitude

Answers

Every 15 degrees along the line of longitude is equivalent to a time difference of 1 hour.

Given that it is 10:00 am at your location when it is noon along the prime meridian, this means that you are 2 hours behind the prime meridian.

The prime meridian is 0 degrees and you are 2 x 15 = 30 degrees west of the prime meridian.

Therefore, your longitude is 30 degrees west.

For every 4 miles vanessa jogged cody jogged 3 miles if vanessa jogged 1 miles how far did cody have jogged

Answers

divide 3 by 4 = 3/4 = 0.75

so Cody jogs 3/4 mile for every 1 mile Vanessa runs

Translate into a numerical expression

The product of fifteen and negative three decreased by twelve.
The sum of three cubed and four.

Answers

(15*-3)-12
3(with another mini three)+4=?

After translating words to numerical form, it is equal to 135.

What is an expression?

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the value provided in the question,

Product of 15 and another number.

Another number is negative 3 decreased by 12 which means that (12 - 3) = 9

Product in numeric form = 15 × 9 = 135

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Tony started a blanket business. He purchased a sewing machine and some fabric to get started, and then sold each blanket for the same price. The expression −450+12x represents the profit that Tony has earned based on the number of blankets sold.

Which expression represents the total amount Tony earns from selling blankets?



12x

12

−450+12x

x

Answers

the answer is 12x Tony earns 12x


The answer is a.


12x


Convert 26.2 mi to kilometers using 1 mi = 1.6 km.

Answers

1mile=1.6 kilometer
26.2miles=26.2*1.6=41.92 kilometers
41.92 is the answer brainiest pls

Kevin is six years older than his twin sisters. The sum of the three children’s ages is the same as their 42 year old dad’s age. How old are the children?

Answers

Let the age of Kevin be x,

age of twin sisters = x - 6
sum of children's age = x + x - 6 + x - 6
= 3x - 12
3x - 12 = 42
3x = 54
x = 54/3
= 18
age of twin sisters = x - 6
= 18 - 6
= 12

Kevin is 18 years old whereas the twin sisters are both 12 years old.
Final answer:

The question involves solving a basic algebra problem to determine the ages of three children. By setting up an equation based on the given information, we find that each twin sister is 12 years old and Kevin is 18 years old.

Explanation:

The question revolves around finding the ages of three children, Kevin and his twin sisters, given that Kevin is six years older than his twin sisters and the sum of their ages equals their father's age, who is 42 years old. First, let's denote the age of each twin sister as x. Since Kevin is six years older, his age will be x + 6. The sum of their ages equals their father's age, which is given as 42 years. Therefore, the equation to find their ages will be:

[tex]x + x + (x + 6) = 42[/tex]

This simplifies to:

3x + 6 = 42

Subtracting 6 from both sides gives:

3x = 36

Dividing by 3:

x = 12

So, the age of each twin sister is 12 years, and Kevin's age is 12 + 6 = 18 years.

A quadrilateral has angles that measure 125°, 115°, and 65°.



What is the measure of the fourth angle?

Answers

the answer is 11 degrees 
Hello! A quadrilateral has 4 angles that equal 360 degrees. You already have three that equal 125 degrees, 115 degrees, and 65 degrees. Those three angles when added up have a sum of 305 degrees. Then, you subtract that number from 360 to find your fourth angle. 360 - 305 = 55. The measurement of the fourth angles is 55 degrees.

A basketball has a radius of 12.5 inchesWhat would be the volume of the basketball?

Answers

To Find The Volume Of A Sphere (Basketball) The Formula Would Be V=4/3πr^3 If You Input 12.5 As r Your Radius Your Answer Would Be 8181.23
Final answer:

The volume of a basketball with a radius of 12.5 inches is calculated using the formula for the volume of a sphere (4/3πr³). The result approximates to 8177.083 cubic inches.

Explanation:

The volume of a sphere, like a basketball, can be calculated using the formula 4/3πr³. Here, r is the radius of the sphere. As specified, the radius of the basketball is 12.5 inches. So, we just need to plug that into our formula:

Volume = 4/3 * π * (12.5)^3  , value of  π is 3.14 approximately.

When you calculate the above expression, you'll find the volume of the basketball is approximately 8177.083 cubic inches.

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What is the slope of a line that is parallel to the line shown?

Answers

Parallel lines have the same slope, so if we find the slope of the line shown, the slope of the line parallel to it will be the same.

To find the slope, we find the rise divided by the run, or the change in x values divided by the change in y values.

slope = m = (y1 - y2)/(x1 - x2) = (3-2)/(0-3) = 1/(-3) = -1/3

Therefore, the slope is -1/3, and so the slope of the parallel line is also -1/3.

Your answer is -1/3.

Hope this helps!

what operation should be performed first to solve this problem?
the Johnson family can fly from Washington DC to London $18 per mile per person. The distance is 3,663 miles. how much will the trip cost if four people go?

A. addition

B. division

C. subtraction

D. multiplication

Answers

The answer is...
D)Multiplication
yes It's D, MULTIPLICATION thank you very much.

Find the length of LM

Answers

Take 36,5x-29, and 2x-21 and add them. Then set them equal to 46+4x. Solve for x and you should get x=20. Now take this value and substitute it into the expression 2x-21 to find LM. Your answer should be 19.

Suppose you feel hungry so you reach for a plum you see in a fruit bowl. explain how both external and internal stimuli are involved in your action

Answers

In the given scenario above, the one who will be named as the external stimulus is the action of having to use the sense of sight when you have seen the fruit of bowl. The internal stimulus will be the action of having to feel the hunger.

The width of a rectangle is 8 inches more than the length. The perimeter is 60. Find the length and width of the rectangle.

Answers

The length is 19 in and the width is 11in

can anyone please factor this v^3+27

Answers

[tex]v^3+27=v^3+3^3=(v+3)(v^2-3v+9)[/tex]

The expression v^3 + 27 can be factored as a sum of cubes using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2). In this case, it factors to (v + 3)(v^2 - 3v + 9).

To factor the expression, v^3 + 27, we recognize it as a sum of cubes. The formula for factoring a sum of cubes is:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, a = v and b = 3 since 27 is 3 cubed (3^3).

Identify the cube roots of each term

Apply the sum of cubes formula:

Substitute the values into the formula:

Hence, we get v^3 + 27 = (v + 3)(v^2 - 3v + 9)

So, v^3 + 27 factors to (v + 3)(v^2 - 3v + 9).

Solve for x
3(5x + 4) - 20 - 13x = -4

Answers

3(5x+4)- 20 - 13x=-4
expand:
(3×5x) + (3×4) - 20 - 13x=-4
15x + 20 - 20 - 13x = -4
simplify:
15x - 13x + 20 - 20=-4
2x=-4
solve:
2x/2=-4/2
x=-2

Value of x is 2, can be determined by algebraic equation.

What is algebraic equation ?

It’s a equation for of known and not known constant and we have to find the not known constant value .

3(5x+4) - 20 -13x

= - 4 15x + 12 - 20 - 13x

= - 4 2x -8

= - 4 2x

= 8 - 4 2x

= 4 x

= 2

Hence , the value of x will be 2 .

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please answer all questions thank you.

Answers

1) 78.5/pi = 25
radius = 5
The one 5 digits away from that coordinate is (2,-1)

2) This question is area, not perimeter. The width and length has to be added by 4 because of 2 feet on both sides.
9*10 = 90 - 30 = 60

3) 25pi according to pythagorean theorem.

What is the domain when a function has an imaginary number?

Answers

The imaginary numbers are often presented on a real-imaginary graph where the imaginary numbers are on the vertical axis. 

A function that has imaginary numbers would have a domain that consists a range of numbers on the horizontal axis. Since the horizontal axis represents real numbers, hence the domain of the function (providing there's no limitation) is all the numbers on the horizontal axis

PLS HELP!!!!
The number line model may be used to simplify which of the following?


A. –1 + 2 = –1

B. –1 + 2 = –3

C. –1 + 2 = 3

D. –1 + 2 = 1

Answers

The answer is D. –1 + 2 = 1

please answer this question today itself

Answers

see attached picture for answer:

Solve for L: S = B + 1/2L

Answers

First get L on the side by itself by subtracting B from both sides. S-B=1/2L. Then multiply both sides by 2. 2S-2B=L

Isolating L, it is found that the solution for L is given by:

[tex]L = 2(S - B)[/tex]

--------------------------

The equation is:

[tex]S = B + \frac{1}{2}L[/tex]

Leaving everything with L on one side, everything without on the other.

[tex]\frac{L}{2} = S - B[/tex]

[tex]L = 2(S - B)[/tex]

Which is the solution for L.

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Write the equation of the line through the given point. Use​ slope-intercept form.
(-6,1);perpendicular to y= -6/5 x -4

Answers

hello : 
let the slope : a    and ; b the slope of the line : y = (-6/5)x - 4
the line that is perpendicular to(-6/5)x-4  so : a×b = - 1 and b = -6/5
so : a = 5/6

 in slope-intercept form of the equation of the line that is perpendicular
 to is : y = (5/6)x +c
contains (-6,1) : 1 =  (5/6)(-6) +c
c = 6
an equation is : y= (5/6)x + 6

A woman standing on a hill sees a flagpole that she knows is 40 ft tall. the angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. find her distance x from the pole.

Answers

let distance form the pole = x  and height of the hill = y ft

now we can set up 2 equayions 
tan 18 = (40-y)/x
tan 14 = y/x

from second equation y = sxtan14  so we have:-
 tan 18  = ( 40 - x tan 14) /  x

x tan 18 = 40 - x tan 14
x(tan 18 + tan 14) = 40

x   = 40 / (tan18 + tan 14)  =  69.66 feet Answer



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