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Exercise

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

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Final answer to the exercise

$\frac{\sqrt{1+x^2}-x}{\sqrt{1+x^2}\left(1+\left(x-\sqrt{1+x^2}\right)^2\right)}$

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  • Find the derivative using the definition
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  • Integrate by partial fractions
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