(6)

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Step 1:

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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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Power rule of derivatives : $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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St

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$\"\"$

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

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$\"\"$

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Therefore, fourth derivative of the function $\"\"$ .

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7)

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Step 2:

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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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Power rule of derivatives : $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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Therefore, fourth derivative of the function $\"\"$ .

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8)

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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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Derivative of the sine function : $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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Derivative of the cosine function : $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$

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Therefore, fourth derivative of the function $\"\"$ .

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Solution :

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

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