consider the function f(x) for which f(e)=7 and f'(e)=6 find h'(e) for the function h(x)=f(x)^x

h'(e)=

Answers

Answer 1

Answer:

[tex]h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e][/tex]

Step-by-step explanation:

Let [tex]h(x) = f(x)^{x}[/tex], the first derivative of the function is found by applying the concept of implicit differentiation:

[tex]h(x) = f(x)^{x}[/tex] (1)

[tex]\ln h(x) = x\cdot \ln f(x)[/tex]

[tex]\frac{h'(x)}{h(x)}=\ln f(x) +\frac{x\cdot f'(x)}{f(x)}[/tex]

[tex]h'(x) = h(x) \cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right][/tex]

[tex]h'(x) = f(x)^{x}\cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right][/tex]

[tex]h'(x) = f(x)^{x-1}\cdot [f(x)\cdot \ln f(x)+x\cdot f'(x)][/tex] (2)

If we know that [tex]x = e[/tex],  [tex]f(e) = 7[/tex] and [tex]f'(e) = 6[/tex], then [tex]h'(e)[/tex] is:

[tex]h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e][/tex]


Related Questions

plz help me thanks so much :)​

Answers

The correct answer is 6
mrs. gorl the answer is 6

Subtract 5x – 2 from –3x +4. O 2x + 2 o 80 – 6 –80 + 2 -80 + 6 +​

Answers

Answer:

8x - 6

Step-by-step explanation:

5x - 2 - (-3x + 4)

1) Distribute

5x - 2 + 3x -4

2) Combine like terms

8x - 6

Answer:

 D: -8x+6

Step-by-step explanation:

(-3x+4)-(5x-2) This is the set up

(-3x-5x)+(4--2) Combine like terms

-8x+6 Simplify

You could produce a pair of like terms with opposite coefficients by multiplying the first equation by what number?

Answers

Answer:

6

Step-by-step explanation:

just did on edge

Answer:

C. 6

Add

-2,-4

YOUR WELCOME ;)

Step-by-step explanation:

EDGE2021

David bought 3 1/3 fabric . How much is this in feet?

Answers

Answer:10 feet, I think

Step-by-step explanation:

HELPPP ME PLEASSSEE :(

Answers

I am pretty sure the answer is d.

Answer:definitely a trinomial expression.

Step-by-step explanation:

Since it has 3, it’s a trinomial.

Write the fraction that would land on point A on the number line.

Answers

1/3

There are six lines. 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6. 6/6 is 1, the last line.

Point A is at 2/6. Since both numbers can be reduced by 2, you divide them both by 2. The final answer would be 1/3.

Item
Price
Markup %
Markup
Retail Price
Shoes
$75.38
39%
$

Answers

The answer is 104.7782 tell me if it’s right

the product of the sum and the difference of 8x and 4y

Answers

Answer:

4

Step-by-step explanation:

o dont really know. I dont understand the question

You can’t solve this because you can’t add or subtract different variables. However you can multiply different variables and it’ll give you 32xy

Which set of ordered pairs below is a function?

A {(3,–2); (5,–3); (7,–4); (9,–5)}

B {(3,–2); (3,–12); (9,–2); (12,–2)}

C {(4,–2); (5,–3); (7,–4); (7,–5)}

D{(4,–2); (4,–3); (4,–8); (4,–9)}

Answers

The answer is A.

Ordered pairs that equate to a function would not have two separate points with the same x-value. In other words, every x-value must be associated with only one y-value.

when ------, you change a number to one that is less exact, so it is easier to work with.


please help me in have 10 minutes left

Answers

Rounding is the correct answer I believe.

The daily low temperatures from last week are shown below. (The measurement is fahrenheit)
-9, -8, -7, 8, 10, 12, 18
What is the mean low temperature of last week?
A.-2
B.6
C.8
D.10

Answers

Answer:

thx for the free points g

One number is 5 greater than another. The product of the numbers is 36.
Find the numbers.

Answers

Answer:4 and 9 are the numbers

Step-by-step explanation:

Answer:

4 and 9

Step-by-step explanation:

Factors of 36 are:

(1x36), (2x18), (3x12), (4x9), (6x6)

The ones with a difference of 5 are 4 and 9, and so therefore they are your answers.

How do you do this question?

Answers

Answer:

y = Ce⁻ᵗ − 7

Step-by-step explanation:

dy/dt = -y − 7

dy/dt = -1 (y + 7)

Separate the variables.

dy / (y + 7) = -1 dt

Integrate both sides.

ln│y + 7│= -t + C

Solve for y.

y + 7 = e⁻ᵗ⁺ᶜ

y + 7 = eᶜ e⁻ᵗ

eᶜ is another arbitrary constant, so:

y + 7 = Ce⁻ᵗ

y = Ce⁻ᵗ − 7


Which of the following statements is NOT equivalent to the statement, 'There exists either a
computer scientist or a mathematician who knows both discrete math and Java.

Answers

Computer Scientist lol I need 20 characters

The correct answer is computer scientists because they know both discrete math and java.

Given that,
"There exists either a computer scientist or a mathematician who knows both discrete math and Java." is to be discussed.

What is java?

Java is a computer programming language, which helps to build software and program on computers.

here,
Mathematicians do have knowledge of discrete math but they do not have known what actually java is, while being a computer scientist one should have knowledge of both discrete math and Java.

Thus, the correct answer is computer scientists because they know both discrete math and java.

Learn more about java here:
https://brainly.com/question/13261090
#SPJ2

What is the slope of the linear table below?

Answers

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 8) and (x₂, y₂ ) = (0, 10) ← 2 ordered pairs from the table

m = [tex]\frac{10-8}{0+3}[/tex] = [tex]\frac{2}{3}[/tex] → A

twice the square of a number

Answers

Answer:

2 * x^2

Step-by-step explanation:

in word form: two times the square of x

"a number" can be any variable; i used x

Answer:

x² × 2

Step-by-step explanation:

Notice vocabulary:

twice → multiplication by a factor of two → ×2a number → unknown number; variable → xthe square → raised to the power of two →

Put this information together.

"Twice the square of a number"

Since it says of a number, this number comes first → [tex]x[/tex]

"Twice the square of a number"

The square of a number means that the variable will be squared → [tex]x^2[/tex]

"Twice the square of a number"

Multiply the variable by a factor of two → [tex]x^2*2[/tex]

:Done

A giant right triangular sculpture has two legs with lengths 20 meters and 40 meters. What is the measure of the smallest angle in this sculpture? Round your answer to the nearest degree.
15°
27°
30°
43°

Answers

Answer:

we have the same question

Step-by-step explanation:

please tell me what you got when you receive an answer

Answer:

30 degrees

Step-by-step explanation:

we need to compute angle A and angle B (see figure below)

hence,

[tex]cosA=\frac{20}{40}\\ cosA=\frac{1}{2}[/tex]

this implies that A=60 degrees.

Since interior angles of a triangle add up 180 then,

A+B+90=180

60+B+90=180

B+150=180

B=180-150

B=30 degrees

which is the smallest angle

Hey, I need this answer in by today. Please help me solve this and give a word by word explanation. Thanks!

Answers

Answer:

185

Step-by-step explanation:

firstly you calculate all in brackets

(280+20)÷3

300÷3

100-15

85

now you calculate 10×5=50

2×50=100

85+100=185

so firstly deal with problem inside the brackets, then you got multiplication and division outside their brackets and finally get 85 +100 =185

Megan makes and sell slime online.

Answers

Answer:

44 containers

How far is the robot claw from the winter lane

Answers

Answer:

4 blocks.

Step-by-step explanation:

D. Find the coordinates of the vertex

Vertex: ( , )

Please anyone helps me

Answers

Answer:

(-2,4)

Step-by-step explanation:

What is the GCF of 8 and 20
O 8
O2
O 4
O 10

Answers

What is the GCF of 8 and 20

Answer: 4

Miss Holman bought a meal that cost $6.25. She gave her server $1.25 tip. What percent did she tip her server?

Answers

Answer:

20%

Step-by-step explanation:

6.25 times 20% or 0.2 = 1.25. therefore she tipped the sever 20% of the total cost of her meal.

Please help someone

Answers

Answer:

root of 64, root of 71,pie squared

Step-by-step explanation:

15 POINTS IF U ANSWER

Answers

Answer:

we need explaining of this question

Graph the set on the number line.

Answers

Here’s the answer w explanation :)

Calculate each unit rate. Round to the nearest hundredth if necessary. 175 Calories in 12 ounces

Answers

Answer:

L

Step-by-step explanation:

The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\_ +/-\(t text( critical value)\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.) (a) 95% confidence, n = 17(b) 90% confidence, n = 12 (c) 99% confidence, n = 24 (d) 90% confidence, n = 24 (e) 80% confidence, n = 13 (f) 95% confidence, n = 10

Answers

Answer:

a) 2.120

b) 1.796

c) 2.807

d) 1.714

e) 1.356

f) 2.262

Step-by-step explanation:

The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\_ +/-\(t text( critical value)\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.)

(a) 95% confidence, n = 17

We find our degrees of freedom first

= n - 1

= 17 - 1

= 16

The t critical value using the t table =

2.120

(b) 90% confidence, n = 12

We find our degrees of freedom first

= n - 1

= 12 - 1

= 11

The t critical value using the t table =

1.796

(c) 99% confidence, n = 24

We find our degrees of freedom first

= n - 1

= 24 - 1

= 23

The t critical value using the t table = 2.807

(d) 90% confidence, n = 24

We find our degrees of freedom first

= n - 1

= 24 - 1

= 23

The t critical value using the t table =

1.714

(e) 80% confidence, n = 13

We find our degrees of freedom first

= n - 1

= 13- 1

= 12

The t critical value using the t table = 1.356

(f) 95% confidence, n = 10

We find our degrees of freedom first

= n - 1

= 10 - 1

= 9

The t critical value using the t table =

2.262

WILL GIVE BRAINLIEST! 2 QUESTIONS FOR 6 POINTS +3 TO WHOEVER ANSWERS QUICKEST! AND THE HAVE A GOOD EXPLAINATION!

1: (THE PICTURE)

POSSIBLE ANSWERS:


Line A

Line B

Line C

Line D


2: The F-16 Fighting Falcon, a United States fighter jet, can travel 3680 miles in 4 hours. In miles per hour, what is the speed of the F-16?

POSSIBLE ANSWERS:

1. 900mph

1. 736mph

3. 460mph

4. 0.001086mph

5. None of the Above

Answers

So pretty much for the first question it is line A since the steeper the line the faster something goes as in this case A is covering the most questions at the fastest rate.


For the second one it’s none of the above because 3680/4=920.


Hopefully I don’t get this wrong :/

how to math pls i ned to math

Answers

Answer:

8 inches

Solution:

First, you need to add all sides which will give you 147. Then, to find the length of GA, you need to subtract the perimeter which is 167, by 147 which will give you 20. GA = 20

Thus to find G'A', you need to cross multiply 14/35 = G'A'/20

You should end up with 280 = 35. Divide 35 by 280 and you get 8.

PLEASE MARK IT AS BRAINLIEST

Answer:

2+2=4-1+3

Step-by-step explanation:

quick mafs

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