$\"\"$

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Derivatives of Inverse Hyperbolic Functions : $\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Apply the chain rule : $\"\"$

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Let $\"\"$ .

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$\"\"$

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Apply common derivative.

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$\"\"$

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$\"\"$

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Substiute back $\"\"$ .

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$\"\"$

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From the trignometric identity : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The derivative of $\"\"$ is $\"\"$ .