If f (x) = sin−1x, then f′(√3/2)= ?

Answer:

[tex]f'(\dfrac{\sqrt3}{2})[/tex] = 2

Explanation:

Given that,

[tex]f(x)=\sin^{-1} x[/tex]

We need to find the value of [tex]f'(\dfrac{\sqrt3}{2})[/tex]

First, we take f'(x). We know that,

[tex]\dfrac{d}{dx}(\sin^{-1} x)=\dfrac{1}{\sqrt{1-x^2} }\\\\f'(x)=\dfrac{1}{\sqrt{1-x^2} }\\\\f'(\dfrac{\sqrt3}{2})=\dfrac{1}{\sqrt{1-(\dfrac{\sqrt3}{2})^2} }\\\\=\dfrac{1}{\sqrt{1-(\dfrac{3}{4})} }\\\\=\dfrac{1}{\sqrt{\dfrac{1}{4}}}\\\\=\dfrac{1}{\dfrac{1}{2}}\\\\=2[/tex]

So, the value of [tex]f'(\dfrac{\sqrt3}{2})[/tex] is 2.

Given that:

We know that,

→ [tex]\frac{d}{dx} (sin^{-1} x) = \frac{1}{\sqrt{1-x^2} }[/tex]

Now,

→ [tex]f'(x) = \frac{1}{\sqrt{1-x^2} }[/tex]

then,

→ [tex]f'(\frac{\sqrt{3} }{2} ) = \frac{1}{1-(\frac{\sqrt{3} }{2} )^2}[/tex]

By opening the square, we get

              [tex]= \frac{1}{\sqrt{1-(\frac{2}{4} )} }[/tex]

              [tex]= \frac{1}{\sqrt{\frac{1}{4} } }[/tex]

              [tex]= \frac{1}{\frac{1}{2} }[/tex]

              [tex]= 1\times \frac{2}{1}[/tex]

              [tex]= 2[/tex]

Thus the above answer is right.

Learn more about function f(x) here:

https://brainly.com/question/17032105

ASAP HELP NEENED!!!!
A member of Congress was recently elected by a very wide margin. The representative does not anticipate any strong opposition in either the primary election or the general election. A piece of legislation that does not directly affect the representative’s district has been introduced. The media are not reporting on this piece of legislation.

(A) Describe the role conception in which the representative is most likely to engage.

(B) In the context of the scenario, explain how the representative’s vote is affected by party leadership in Congress.

(C) In the context of the scenario, explain how interest groups might affect the representative’s vote on the legislation and the position of the majority party.

Refer to the passage.

It is my intention to curb the size and influence of the federal establishment and to demand recognition of the distinction between the powers granted to the federal government and those reserved to the states or to the people. All of us need to be reminded that the federal government did not create the states; the states created the federal government.

–President Ronald Reagan,
First inaugural address,
January 20, 1981

Which of the following scenarios would most likely have been opposed by the Republican Party during the Reagan administration?

A member of Congress introduces a bill to reduce tax rates for all income groups.
The AARP lobbies for the expansion of Medicare to cover more people and provide more services.
A coalition of governors requests that Congress change a federal welfare program from a categorical grant to a block grant.
The president proposes a budget that reduces federal spending on education and health care, areas traditionally controlled by state governments.

Ano ang mga paraan para makaiwas sa kalamidad Pagkatapos ng kalamidad​

which of the following best describes a species?

Which of the following regions experiences its greatest solar intensity in late December?

Refer to the table.



Based on the data, which of the following outcomes is most likely when people vote or run for office?

Voters will support policies that match the misinformation on immigration.
Officials will expend resources informing voters of the correct facts about immigration.
Immigration will be ignored in most debates in favor of topics that the public is better informed about.
Candidates will support immigration policies without regard for public opinion due to a lack of quality data.

Which of the following was not an economic effect of colonization?
A. Privileged access to colonial markets
B. A one-way flow of wealth
C. Global economic development
D. Greater trade restrictions

URGENT PLEASE HELP?!
Which statement best describes the purpose of judicial review?
O It limits the types of cases the Supreme Court can hear.
It allows the Supreme Court to have original jurisdiction in some cases.
O It mandates that state courts can overturn federal actions in their jurisdictions.
O It provides a check on the power of the executive and legislative branches of government.

Overgrazing is a condition of which type of land grazing?
A) one that is conditional to the climatic conditions in the associated region
B) one where the maximum number of species per unit area is decreased
C) a type of traditional herding where practices are employed
D) a type where ranchers want to increase the amount of cattle production
E) one that creates a paradigm where diversity is reduced and vegetation growth slows