Prove d/dx(a^x) = a^x ina

Answers

Answer 1

Answer:

yw

Explanation:

Let :ℝ→ℝ be given by ()= and consider the ln function. We can take the composition so that we have:

(ln∘)()=ln(^)=ln

Now, if we take the derivative, on the left hand side we use the chain rule and on the right hand side we differentiate as usual so that we have:

′()/()=ln

Now solving for ′() gives ′()=()ln so that ′()=^ln. This useful technique can be used to take derivatives of other functions: we compose the original function with the inverse and then differentiate on both sides and use the same idea we've used here, this technique can simplify many derivatives and save a lot of time in some situations.


Related Questions

The stock market experienced massive growth following President Trump's election in 2016, surging
nearly 38%. Explain how or if this specific event affected Aggregate Demand.

Answers

"Big Tech has faced a lot of scrutiny, and the sector's expectations are currently fairly low. In their earnings speech, Big Tech companies should concentrate on profitability and cost-cutting initiatives.

What is Stock market?

Wednesday's financial reports are expected to be reported by Boeing, Hilton Worldwide, and Spirit Airlines before the market opens. Meta Platforms, eBay, and Mattel are scheduled to report following the closing.

The Dow lost around 344 points on Tuesday, and traders are coming off a dismal session. The Nasdaq Composite fell almost 2%, and the S&P 500 ended 1.6% lower.

In the first quarter, First Republic Bank reported that their deposits decreased by 40% to $104.5 billion. This rekindled worries about the larger banking industry, which put Tuesday's key averages under pressure.

Therefore, "Big Tech has faced a lot of scrutiny, and the sector's expectations are currently fairly low. In their earnings speech, Big Tech companies should concentrate on profitability and cost-cutting initiatives.

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What organization created the Occupational Outlook Handbook?

CareerOneStop
O*NET
the BLS
a CTSO

Answers

The organization that created the Occupational Outlook Handbook is: C. the BLS.

What is O*NET?

O*NET is an abbreviation for occupational information network and it can be defined as an online database or free resource center that is updated with several occupational definitions on a timely basis, so as to help the following categories of people understand the current work situation in the United States of America:

Job seekersWorkforce development professionals.Business firmsStudentsHuman resource (HR) managers

What is BLS?

BLS is an abbreviation for Bureau of Labor Statistics and it can be defined as an organization created by the national government of the United States of America.

Generally speaking, the Bureau of Labor Statistics (BLS) is saddled with the responsibility of creating the Occupational Outlook Handbook and ensuring that the labor rights of American citizens are enforced throughout the United States of America.

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The _______ would activate our fight or - flight response to encountering a bear on our walk.

Referring to “what” section of the brain

Answers

Answer: Amygdala

Explanation: The amygdala activates this fight-or-flight response without any initiative from you. When that part of your brain senses danger, it signals your brain to pump stress hormones, preparing your body to either fight for survival or to flee to safety.

Upon returning from a year long working holiday, Alberta, the youngest of 4 sisters, announced her whirlwind marriage. Her 3 sisters, Carla, Paula, and Roberta, were amazed by her husband’s name.
The 4 men are Albert, Carl, Paul, and Robert. Their last names are Albertson, Carlson, Paulson, and Robertson.
No woman’s husband has a first name that consists of her first name without the final “a”; no woman’s last name consists of her first name without the final “a” and with “son” on the end; and, no man’s last name consists of his first name with “son” added at the end.
Paul is not married to Roberta, and Robert is not married to Paula.
No husband and wife have “bert” in both their first names, but there is a man who has “bert” in his first and last names.
Carl’s last name is not Paulson.

Answers

Answer:

Explanation:

Alberta husband is Paul because she cannot be marry to Robert and Albert

Upon returning from a year-long working holiday Paul is Alberta's husband because she can't wed Robert or Albert.

What is the holiday?

The Old English term "holiday" (hlig "holy" + dg "day") is where the word "holiday" first appeared. The phrase's original meaning was limited to holy days. The modern application differs regionally. It refers to any designated holiday or season of celebration in North America.

Returning from a year-long working holiday Paul is Alberta's husband because she can't wed Robert or Albert. Alberta, the youngest of 4 sisters, announced her whirlwind marriage.

Therefore, Upon returning from a year-long working holiday Paul is Alberta's husband because she can't wed Robert or Albert.

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How much profit will you earn if you increase your price $10 higher than market price?

Answers

The profit that will be earned when there's an increase your price of $10 that is higher than market price is $100.

What is the market price?

The market price is the current cost of purchasing or selling an asset or service. The dynamics of supply and demand influence the market price of an item or service. The market price is the price at which quantity provided equals quantity desired.

The assumed market price of a good is given as $20 and 40 quantities are sold. The producer decides to increase the price by $10 and the quantity demanded will reduce by 10.

New price = $20 + $10 = $30

New Quantity = 40 - 10 = 30

The profit will be calculated thus:

= New Revenue - Old revenue

= ($30 × 30) - ($20 × 40)

= $900 - $800

= $100

Note that an overview was given as the information is incomplete.

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list and explain five factors that can contribute to an economy’s growth

Answers

Answer:

-An economy can grow when there is an increase in the productivity of labor. This means that more output can be produced with the same amount of input, or the same amount of output can be produced with less input.

-An economy can also grow when there are increases in capital investment, such as factories and machinery.

-Natural resources may contribute to economic growth if they are exploited effectively.

-The size of a country’s population affects its potential for economic growth – a larger population generally indicates a greater potential workforce and consumer base.

-Last but not least, technological advances usually lead to increased efficiency and higher levels of production across most sectors

A conflict or discrepancy between the specifications and the drawings gets resolved by using
an as-built drawing.
a request for information.
an email to the inspector.
a call to the manufacturer.

Answers

If there is a conflict or discrepancy between the specifications and the architectural drawings gets resolved by using: a request for information.

What is architecture?

Architecture can be defined as a special form of art that typically involves the process of planning, designing, developing, and construction of a building or other structures such as residential houses, Church, Mosque, Shopping mall, etc.

What is an RFI?

In Architecture and Construction, RFI is an abbreviation for request for information (RFI) and it can be defined as a formally written document which is used by project managers, architects, structural engineers and civil engineers, etc., to seek a better clarification on specifications, plans, architectural drawings, and agreements.

In conclusion, a request for information (RFI) is a formal document which can be used to resolve any form of conflict or discrepancy between the project specifications and the architectural drawings, especially by seeking to clarify all information gaps within any construction document.

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How can families and educators work together to improve education ?​

Answers

Answer: I think the family and the educators can improve education because they have there mind set on it.

Explanation:

In the final paragraph, the sentence “The red percussion of their fires could be seen night and day by those waiting in the dark trance of the frozen town” serves to highlight contrasts between all of the following EXCEPT from “First Love”

Answers

Answer: e. the vulnerability of wildlife and the resilience of humans

Ethics of Journalism

1. What are they? List them out (5 of them)

2. Explain your thoughts on each one (even if you don't understand it...write questions about each one).

3. Which is most important? Why?

Answers

Answer:

seek truth, minimize harm, act independently, Be accountable and Transparent

Explanation:

Ethics of Journalist are comprised principles of ethics and good practice applicable to journalists

Federalism is a vital component to the creation of the U.S. constitutional system.
a. Identify and explain two reasons for and against this division of authority.
b. Describe two ways federalism has been challenged over time. Include an
example that deals with a prominent case of the Supreme Court.

Answers

a) Two reasons for federalism include the fact that it allows for a division of powers between the national government and the states. This division of powers allows for a check and balance system, which can help to prevent any one group from having too much power. Additionally, federalism allows for a degree of customization and flexibility, as states can tailor their laws and regulations to better suit the needs of their citizens. Two reasons against federalism include the fact that it can lead to a duplication of services and a waste of resources. Additionally, federalism can sometimes lead to a lack of clarity regarding which level of government is responsible for certain issues. This can lead to confusion and frustration among citizens.

b) Federalism has been challenged over time in a number of ways. One example is the Supreme Court case of National Federation of Independent Business v. Sebelius, in which the Court ruled that the federal government could not require states to expand their Medicaid programs. This case demonstrated the limits of federal power under the Constitution.

Federalism:

Federalism is a hybrid or compound method of governance in which a general administration and regional governments coexist in a single political system, with powers divided between the two. Federalism in the contemporary age was born in the unions of states that existed during the Old Swiss Confederacy.

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Which of the following shows the factor of 5x 2 squared + 17x 6?

Answers

The factor of 5x 2 squared + 17x 6 include (5x + 2)(x + 3).

How to calculate the factors?

A factor is a number that divides another number by itself and leaves no residue. In other words, if multiplying two whole numbers yields a product, the numbers being multiplied are factors of the result since the product is divisible by them.

From the information, the expression given is illustrated as:

5x² + 17x + 6

It's important to note that an expression is a statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Therefore, the expression will be factored thus:

5x² + 17x +6

5x² + 15x + 2x + 6

5x(x + 3) + 2(x + 3)

(5x + 2)(x + 3)

The factors are illustrated above.

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The sum of a whole number A and a whole number B is 12, and the ratio A : B is equivalent to 1 : 3. Find A and B.

Answers

Answer:

A = 3 ; B = 9

Explanation:

A + B = 12

a/b = 1/3

b = 3a

(3) + (9) = 12

(3)/(9) = 1/3

(9) = 3(3)

Answer- A = 3

B = 9

Explanation

1+3 = 4

12 ÷ 4 = 3

A:B

1:3

A = 1×3

B = 3×3


Use log, 30.563, log, 5 0.806, and log, 7 1.042 to approximate the value of the given logarithm to 3 decimal places. Assume that b>0 and b +1.
14
✓15

Answers

Answer:

1.605

Explanation:

Log rules: logb(x*y) = logb(x) + logb(y)

So working with what you're given, x=3 and y=7 so that x*y=21

logb(21)=logb(3)+logb(7)

logb(21)=0.563+1.042=1.605

Solve negative 2 times y plus seven fifths times y equals negative 4 minus three fifths times y minus 2 for y.

y = 0

y = −13

No solution

Infinite solutions

Answers

Answer:

There is no solution to this

Explanation:

Hope this helps you.
I tried to build up what the problem could look like
and this is the answer i got for it. So there C. No Solution.

2 points

Abela often finds herself dreaming about completing college and starting a satisfying career. This experience is in line with Sigmund Freud's belief that dreams serve as a form of
A. hope recognition.
B. ability processing.
C.goal orientation.
D.wish fulfillment.

Answers

It should be


D- wish fulfillment

INTRO TO PSYCHOLOGY

Describe at least 4 environmentally influenced learned behaviors using your own life experience.

Answers

Your environment influences who you are and the actions you may take. The question is asking you to choose four behaviors you have learned by your surroundings that affect your life.

Some examples are;
1. the customs of the place where you grew up (your household rules/school rules/town rules etc.)

2. The people close to you and what you have learned from them maybe certain methods on how to do things

3. Trends, popular activities, clothing styles, slang

4. Education, what you have learned in school that has influenced what you do (having to ask to go to the bathroom, finding the best methods to study or do homework, or even being afraid of failure)

Answer:

One of the learned behaviors that I have learned through environmental change is to only toss the trash in the trash can and to use as little plastic as possible.

To eliminate smog and other hazardous inhalers, environmentally friendly practices should be adopted.

The Examples are:

The first could be the parental influence, in that it is in genetics. My mother used to wake up early have a bath and then used to do regional rituals every day she put this habit into me and the habit is still with me and I love doing it with my mother.

Another example could be cultural influences, such as how my family's habits, traditions, and customs shaped my behavior and how I now do similar things. My personal values, the way I speak, and the way I dress.

Explanation:

What is the null hypothesis if students who had chocolate before exam earned a mean score of 77 with a variance of 15 compared to a mean score of 72 and a variance of 17 for those who did not have chocolate before exam?

Answers

Chocolate may energise the mind to think better
That’s just me tho

1. Under what circumstances were abortion allowed in Texas 1969?


2. What did the Texas District court judges rule in wade legal case

3. What constitutional arguments did coffee and weddington use?

Answers

1. Abortion was allowed in Texas in 1969 if the pregnancy posed a threat to the woman's life or health.

2. The Texas District Court judges ruled that abortion was legal in the Wade legal case.

3. The constitutional arguments used by coffee and weddington were that abortion was a right protected by the Constitution.

Texas:

Texas is a state in the United States' South Central region. With a total size of 268,596 square miles (695,662 km2) and a population of more than 29.1 million people in 2020, it is the second-largest state in the United States in terms of both area (after Alaska) as well as population (after California). Texas borders Louisiana to the east, Arkansas to the northeast, Oklahoma to the north, New Mexico to the west, as well as the Mexican states of Chihuahua, Coahuila, Nuevo León, and Tamaulipas to the south and southwest, as well as the Gulf of Mexico.

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