$\"\"$

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The functions are $\"\"$ , $\"\"$ and the interval is $\"\"$ .

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The extended mean value theorem to the functions $\"\"$ and $\"\"$ in the interval $\"\"$ is $\"\"$ .

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Here $\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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

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$\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$ .

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

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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The extended mean value theorem to the functions $\"\"$ and $\"\"$ in the interval $\"\"$ is $\"\"$ .

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Substitute corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, the value of $\"\"$ .

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$\"\"$

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The value of $\"\"$ .