If x^(y)=5^(x-y) then dy/dx=​

If X^(y)=5^(x-y) Then Dy/dx=

Answers

Answer 1

First, rewrite

[tex]x^y=e^{\ln x^y}=e^{y\ln x}[/tex]

[tex]5^{x-y}=e^{\ln5^{x-y}} = e^{\ln(5)(x-y)}[/tex]

Now, differentiate both sides using the chain rule:

[tex]\dfrac{\mathrm d\left(e^{y\ln x}\right)}{\mathrm dx}=\dfrac{\mathrm d\left(e^{\ln(5)(x-y)}\right)}{\mathrm dx}[/tex]

[tex]e^{y\ln x}\dfrac{\mathrm d(y\ln x)}{\mathrm dx}=e^{\ln(5)(x-y)}\dfrac{\mathrm d(\ln(5)(x-y))}{\mathrm dx}[/tex]

[tex]x^y\left(\dfrac{\mathrm dy}{\mathrm dx}\ln x+y\dfrac{\mathrm d(\ln x)}{\mathrm dx}\right)=\ln(5)5^{x-y}\left(\dfrac{\mathrm d(x)}{\mathrm dx}-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]

[tex]x^y\left(\ln x\dfrac{\mathrm dy}{\mathrm dx}+\dfrac yx\right)=\ln(5)5^{x-y}\left(1-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]

[tex]\left(x^y\ln x+\ln(5)5^{x-y}\right)\dfrac{\mathrm dy}{\mathrm dx}=\ln(5)5^{x-y}-yx^{y-1}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\ln(5)5^{x-y}-yx^{y-1}}{x^y\ln x+\ln(5)5^{x-y}}[/tex]


Related Questions

Which is true when you rent?
ОА.
You build equity in your house.
ОВ.
You are responsible for any repairs.
Ос.
You pay fewer up-front costs.

Answers

You are responsible for any repairs.

Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value between 29.0 and 55.0. Use Table IV in Appendix C to compute the probabilities. Round your answer to four decimal places.

Answers

Answer:

i think it is between 22 and 35

Step-by-step explanation:

The red-tailed tropic bird, Phaethon rubricauda, is an extremely rare sea bird that nests on several islands of the Queensland coast of Australia. As part of a conservation e ort to manage these endangered birds, every nesting pair was measured and weighed. Below are the body weights of these birds (in kg).

Female 2.45 2.57 2.81 2.37 2.01 2.50 2.32
Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84

Required:
a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.
b. Determine the mean, variance, and standard deviation for the male weights.

Answers

Answer:

This is a population

a) Female

Mean : 2.432857143kg

Variance: 0.05162040817kg

Standard deviation: 0.2272012504kg

b) Male

Mean : 2.641428571kg

Variance : 0.03432653062kg

Standard deviation: 0.1852742039kg

Step-by-step explanation:

a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.

a) Female: 2.45 2.57 2.81 2.37 2.01 2.50 2.32

Mean

The formula = Sum of term/ Number of terms

Mean = 2.45 + 2.57 + 2.81 + 2.37 + 2.01 + 2.50 + 2.32/7

17.03/7

= 2.432857143kg

Variance

This is a population

Hence: The formula for Population variance =

= (X - Mean)²/N

Where N = Number of terms = 7

= (2.45 - 2.432857143)² + (2.57 -2.432857143)² + (2.81 -2.432857143)² + (2.37- 2.432857143)²+ (2.01 - 2.432857143)²+ (2.50 - 2.432857143)² + (2.32 - 2.432857143)² /7

= 0.0002938775509 + 0.01880816325 + 0.1422367347 + 0.003951020409 + 0.1788081633 + 0.004508163265 + 0.0127367347/7

= 0.3613428572/7

= 0.05162040817kg

Standard Deviation

Formula = √Variance

= √0.05162040817

= 0.2272012504kg

b. Determine the mean, variance, and standard deviation for the male weights

Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84

Mean

The formula = Sum of term/ Number of terms

= 2.86 + 2.65 + 2.75 + 2.60 + 2.30 + 2.49 + 2.84/7

= 18.49/7

= 2.641428571 kg

Variance

= ( 2.86 -2.641428571)² + (2.65 - 2.641428571)² + (2.75 -2.641428571)² + (2.60 +2.641428571)² + (2.30 - 2.641428571)² + (2.49+2.641428571)² (2.84 + 2.641428571)²/7

= 0.0477734694 + 0.00007346938775 + 0.01178775511 + 0.001716326531 + 0.1165734694 + 0.02293061224 +! 0.03943061226/7

= 0.2402857143/7

= 0.03432653062kg

Standard Deviation

= √Variance

= √0.03432653062

= 0.1852742039kg

An investigation of wages paid to its employees by a large company was undertaken as a result of an allegation of discrimination. Data was collected for 1000 randomly selected employees. The data included employee ID, gender, race, annual wages in dollars (Salary), whether the employee had full-time status or part-time status (Full_Part), number of years of education (Ed), and number of years with the company (Tenure). The first two rows of data in the worksheet are displayed below.
1 Gender Race Salary Full_Part Ed Tenure
2 Female Caucasian 32196 Full 14 2
3 Male Black 62385 Full 16 10
How many cases does this data set contain?
How many variables does this data set contain? (3 p)
How many quantitative variables does this data set contain, and what are they? How many qualitative variables does this data set contain, and what are they?

Answers

Answer:

Step-by-step explanation:

First, the data set is:

  Gender     Race        Salary   WorkTimeStatus   Education   Tenure

1. Female  Caucasian  32196     Full Time                     14yrs          2 yrs

2. Male      Black          62385    Full Time                     16yrs         10yrs

Now to the questions:

(A) This data set contains 2 cases; 1 for the first employee (the female caucasian) and 2 for the second employee (the male black).

(B) This data set contains 6 variables;

1. Gender  2. Race  3. Salary  4. Work time status  5. Years of education

6. Number of years in/with the company

(C) Out of these 6 variables, the quantitative ones (those that can be measured or weighted numerically) are:

3. Salary   5. Years of education   6. Years with the company

Altogether, 3 in number

(D) The qualitative variables are:

1. Gender   2. Race   4. Work Time Status

Altogether that's 3 variables

Can you guys help me with this angle problem for Geometry tysm

Answers

Answer:

You need to solve for x

Step-by-step explanation:

3x + 5 + 10x - 7 = 180

13x + 5 - 7 = 180

13x - 7 = 175

13x = 182

x = 14

Plug in x

3(14) + 5 for QRT and 10(14) - 7 for TRS

QRT = 47 and TRS = 133

Answer:

QRT = 47

TRS = 133

Step-by-step explanation:

The two angles form a straight line so they add to 180

3x+5 + 10x-7 = 180

13x-2 =180

Add 2 to each side

13x-2+2 =180+2

13x= 182

Divide by 13

13x/13 = 182/13

x =14

We want QRT = 3x+5 = 3*14+5 = 42+5 = 47

TRS = 10x-7 = 10*14-7 = 140-7 = 133


A scale drawing of a building needs to be made using the scale 1 in = 230 ft. How tall will the building in the scale drawing be if the building is 1380 ft tall?

Answers

1380/230 = 6 inches in the scale drawing

Two sides of a triangle are equal in length. The length of the third side exceeds the length of one of the other sides by 3 centimetres. The perimeter of the triangle is 93 centimetres. Find the length of each side of the triangle

Answers

Answer:

it must be 30, 30, 33

Step-by-step explanation:

first, divide 93 by 3, since a triangle has 3 sides, you would get 31, yet if you took away that three in 93, it'd be 30. For that one that exceeds the others by 3, add the three to one of the thirds, and the other two are just the same, so when it said, "exceeds the length of one of the other sides," It didn't really change anything, because the other side is just as long.

What is the measure of ZRIA?
R
PA
N
999
.
A. 55
B. 30°
O C. 95°
D. 60°

Answers

The answer would be A

The measure of angle RIA is 55 degrees, option A is correct.

What is Coordinate Geometry?

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the measure of angle RIA

The opposite angle of RIA is LIK

Let us find the measure of LIK

∠FIL+∠LIK+∠KIN=180

30+∠LIK+95=180

∠LIK + 125 =180

Subtract 125 from both sides

∠LIK = 180 - 125

=55 degrees

∠LIK is equal to ∠RIA

∠RIA = 55 degrees

Hence, the measure of angle RIA is 55 degrees, option A is correct.

To learn more on Coordinate Geometry click:

brainly.com/question/27326241

#SPJ5

Graph the line that represents the equation

Answers

Answer:

In the attachment.

Step-by-step explanation:

We need only two points.

Choose any two values of x. Put them to the equation and calculate the value of y:

[tex]y=-\dfrac{2}{3}x+1\\\\\text{for}\ x=0\\\\y=-\dfrac{2}{3}\cdot0+1=0+1=1\to A(0;\ 1)\\\\\text{for}\ x=3\\\\y=-\dfrac{2}{3}\cdot3+1=-2+1=-1\to B(3;\ -1)[/tex]

Multiply. Do not round your answer.
2.48x8.62 =?

Answers

Answer:

21.3776

Step-by-step explanation:

Answer: 21.3776

This is what I got for the answer hope it helps.

The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?

Answers

Answer:

21 sheets of paper

Step-by-step explanation:

If its basically 6 tickets to a piece of paper then you just divide 125 tickets by 6 and get 20.833.... Then your round to the nearest sheet which is 21.

Hope this helps!

Answer:

Approx. 21 sheets of paper

Step-by-step explanation:

1 sheet of paper is used to make 6 tickets

6 tickets = 1 sheet

If 1 sheet is used to make 6 tickets. The number of sheets used to make 125 tickets will more.

if

6 tickets = 1 sheet

125 tickets = (125÷6) × 1

= 20.83333333333

One box of pencils costs rupees 28 . What is the cost of 509 boxes

Answers

Question:

One box of pencils costs rupees 28 . What is the cost of 509 boxes

Given:1 pencil costs=₹281 pencil costs=₹28No. of boxes=509

We know:

Costs of total no. of pencil boxes

=1 pencil box's costs×No. of boxes

=509×28

=14252✓

adult men weights mean of 190 30 3 random men mean weight

Answers

Answer:

is this the question ?

Step-by-step explanation:

Write 1/8% as a decimal number Enter your number in the box

Answers

Answer:

it is 0.125

Step-by-step explanation:

......................

I’m not well with percentages lol. Can someone help me with solving it and answer

Answers

Answer:

1. Dracula Answer: D) 12.5%

2. Jack-O-Lantern Answer: D) 40%

Step-by-step explanation:

1. 54 - 48 = 6

  6/48 = 0.125 x 100 = 12.5%

2. $20 - $12 = 8

    8/20 = 0.4 x 100 = 40%

PLZ HURRY IT'S URGENT!!!
Write the equation of a line with a slope of -2 and a y-intercept of 3.
options:

y=3x−2

y=−3x+2

y=2x−3

y=−2x+3

Answers

Answer:

y=-2x+3

Step-by-step explanation:

please answer....writing assignment for math

Answers

Answer:

This information tells me that f equals a number and 3 multiplied by the number that f equals is 16.

Could I please have Brainliest?

Brandon enters bike race. He bikes 9 1/2 miles every 1/2 hour

Answers

Since there is no table given I will assume that what you want me to do is to show that Unit rate of Brandon’s biking. SO here are the data that we need: => 8 and ½ miles = 8.5 miles => ½ hour = .5 hours or 30 minutes Now, let’s solve for the unit rate => SO in every 30 minutes he bikes around 8.5 miles => Since 1 hour is equals to 30 minutes, simply multiply 8.5 by 2 => 8.5 * 2 = 17miles => 17 miles / hour
Hope this helps:)

The variables x and y are related proportionally. When x = 8, y = 20. Find y when x = 80.

Answers

Answer:

y = 200

Step-by-step explanation:

Use the equation y = kx, where k is a constant.

Plug in the given x and y values, then solve for k:

y = kx

20 = k(8)

2.5 = k

Then, plug in k and the given x value, and find y:

y = 2.5x

y = 2.5(80)

y = 200

So, y = 200 when x = 80

PLEASE HELP! 6TH GRADE MATH please write done what number you're doing

Answers

Answer:

# 10 is 4/3 or 1 and 1/3

#11 is 4/10 or 2/5

#12 is 2 and 3/4

#13 is 36/12 or 3 and 1/12

Step-by-step explanation:

i am not 100% sure on #13 btw

hope this helped!

p.s it would be cool if you gave me brainliest.

Answer:

Hey your answers on there are correct.

Step-by-step explanation:

Carrie has $500 in her bank account. She plans to add $245 a week to her account. Jose has $710 in his bank account. He plans to add $230 a week. How many weeks will it take untill carrie & jose have an equal ammount of money saved up is neither of them spent any of their savings?

Answers

Answer:

14 weeks

Step-by-step explanation:

14 times 245= 3430+ 500=3930 (carrie)

14 times 230= 3220+ 710= 3930 (jose)

List the numbers in order from least to greatest.
-4,8,-15,-8,4,1
The numbers in order from least to greater Are

Answers

Answer: -15, -8, -4, 1, 4, 8

Assemble the proof by dragging tiles to the statements and reasons columns

Answers

Answer:

Here, I did the assignment. I wish you good luck!

-
y=2/3x + 2 and passes through the point (12, 6).
Find an equation perpendicular to the line
A. y=-3/2x + 21
B. y=-3/2x +24
C. y= 2/3x + 14
D. y= 2/3x + 8

Answers

Answer:

B. y = -3/2x + 24

Step-by-step explanation:

The perpendicular slope is -3/2x to find the y-intercept use the point given

Plug in

6 = -3/2(12) + b (b = y-intercept)

6 = -18 + b (add 18 on both sides)

24 = b (so)

y = -3/2x + 24

I need help on math​

Answers

what is the question ?

can anyone help me ​

Answers

Answer:

A

Step-by-step explanation:

What is 5/8 of $16 restaurant bill=
What is the answer

Answers

Answer:

$10

Step-by-step explanation:

16 * 5 / 8 = 16 * 0.625 = $10

pls help meeeeeeeeeeee!!

Answers

Answer:

45 with a remainder of 27.

Step-by-step explanation:

Hope this helps you! Good luck! <3

Solve for x.
x-4/5= -1/3

Answers

Answer:

x = 1 2/15

Step-by-step explanation:

Write the equation of the line parallel to the given line and through the given
point. y=2x - 8 through (3.10)

Answers

Answer:

y-2x -8

Step-by-step explanation:

your jus gonna right it back because it's parallel which means it's the same thing.

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