# What is the derivative of #y=arcsin(x/3 )#?

Simplifying yields:

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The derivative of ( y = \arcsin(\frac{x}{3}) ) with respect to ( x ) is:

[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - \left(\frac{x}{3}\right)^2}} \times \frac{1}{3} = \frac{1}{3\sqrt{1 - \left(\frac{x}{3}\right)^2}} ]

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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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