# What is the derivative of #arctan(x - sqrt(1+x^2))#?

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So,

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The derivative of ( \arctan(x - \sqrt{1+x^2}) ) is ( \frac{1}{1+(x - \sqrt{1+x^2})^2}\left(1-\frac{x}{\sqrt{1+x^2}}\right) ).

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The derivative of ( \arctan(x - \sqrt{1+x^2}) ) is ( \frac{-1}{\sqrt{1+x^2} \cdot \sqrt{2 - 2x - 2\sqrt{1+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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