# How do you differentiate # f(x) = (1+x^2) arctanx #?

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To differentiate ( f(x) = (1+x^2) \arctan(x) ), you would use the product rule. The derivative would be:

[ f'(x) = (1+x^2) \frac{d}{dx}(\arctan(x)) + \arctan(x) \frac{d}{dx}(1+x^2) ]

[ f'(x) = (1+x^2) \left(\frac{1}{1+x^2}\right) + \arctan(x) (2x) ]

[ f'(x) = 1 + 2x \arctan(x) ]

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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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