# How do you find the derivative of the function: #arcsin(sqrt(2x-1))#?

The derivative is

Therefore,

So,

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To find the derivative of the function arcsin(sqrt(2x-1)), you can use the chain rule.

Let u = sqrt(2x-1).

Then, differentiate u with respect to x to find du/dx.

Next, find the derivative of arcsin(u) with respect to u, which is 1/sqrt(1-u^2).

Finally, multiply du/dx by 1/sqrt(1-u^2) to obtain the derivative of arcsin(sqrt(2x-1)) with respect to x.

Putting it all together, the derivative is:

(1/sqrt(1-(sqrt(2x-1))^2)) * (1/(2*sqrt(2x-1)))

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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