# How do you differentiate # g(x) = sin (arctan (x/sqrt(3))) #?

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To differentiate ( g(x) = \sin(\arctan(x/\sqrt{3})) ), you can use the chain rule.

Let ( u = \arctan(x/\sqrt{3}) ). Then ( \frac{du}{dx} = \frac{1}{1+(x/\sqrt{3})^2} \cdot \frac{1}{\sqrt{3}} ).

Now differentiate ( g(x) = \sin(u) ) with respect to ( u ), and then multiply by ( \frac{du}{dx} ) to get the final derivative.

( \frac{dg}{dx} = \cos(\arctan(x/\sqrt{3})) \cdot \frac{1}{1+(x/\sqrt{3})^2} \cdot \frac{1}{\sqrt{3}} ).

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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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