$\"\"$

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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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$\"\"$

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$\"\"$ .

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The function is $\"\"$ .

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The $\"\"$ function is defined for all values of $\"\"$ .

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The Domain of the function is $\"\"$ .

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Hence the one of the largest interval is $\"\"$ .

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$\"\"$

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$\"\"$ .

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Write the derivative as a function of $\"\"$ .

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$\"\"$ .

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Trigonometric identities : $\"\"$ .

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Substitiute $\"\"$ in the function $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the function $\"\"$ .

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$\"\"$ .

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$\"\"$

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

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The one of the largest interval is $\"\"$ .

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