# How do you find the derivative of #arctan^-1 (1/(1+x^2))#?

The derivative is

We need

Then,

Differentiating both sides

Therefore,

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To find the derivative of ( \arctan^{-1} \left( \frac{1}{1+x^2} \right) ), apply the chain rule. Let ( u = \frac{1}{1+x^2} ). Then, differentiate ( u ) with respect to ( x ), and substitute the result into the derivative of ( \arctan^{-1}(u) ). The derivative is ( \frac{-2x}{(1+x^2)^2 + 1} ).

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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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