# What's the derivative of #arctan (x/2)#?

Substitute these values into (A) and convert u back into terms of x.

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The derivative of ( \arctan\left(\frac{x}{2}\right) ) with respect to ( x ) is:

[ \frac{1}{1 + \left(\frac{x}{2}\right)^2} \cdot \frac{1}{2} ]

This simplifies to:

[ \frac{1}{2 + x^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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