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

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

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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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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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.

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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