$\"\"$

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The function is $\"\"$ .

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The function can be written as $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Take natural logarithm on both sides.

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$\"\"$ .

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Quotient rule of logarthm: $\"\"$ .

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$\"\"$ .

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Apply derivatine on both sides.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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$\"\"$ is proved.