# How do you find the derivative of #y = arctan(x^2)#?

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To find the derivative of ( y = \arctan(x^2) ), use the chain rule. First, differentiate the outer function (\arctan(u)), where ( u = x^2 ), with respect to ( u ), and then multiply by the derivative of ( u = x^2 ) with respect to ( x ).

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

Therefore, the derivative of ( y = \arctan(x^2) ) is ( \frac{2x}{1 + x^4} ).

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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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