# What is the derivative of #arcsin sqrt(2x)#?

The derivative is

Let

The goal is to solve for

Take the derivative of each side with respect to

We need to know what

From the diagram

Alternatively, use the chain rule.

Given,

Let

Substitute

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The derivative of arcsin(sqrt(2x)) is 1 / (sqrt(1 - 2x) * sqrt(2x)).

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The derivative of arcsin(sqrt(2x)) is 1 / sqrt(1 - 2x).

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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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