# How do you find the derivative of #y = arcsin(3x + 4)#?

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To find the derivative of ( y = \arcsin(3x + 4) ), you can use the chain rule. The derivative is given by:

[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - (3x + 4)^2}} \cdot \frac{d}{dx}(3x + 4) ]

After taking the derivative of (3x + 4) with respect to (x), which is simply (3), the expression simplifies to:

[ \frac{dy}{dx} = \frac{3}{\sqrt{1 - (3x + 4)^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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