(a)

The function is .

Find .

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Apply derivative on each side with respect to .

Product rule of derivatives : .

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Apply second derivative on each side with respect to .

.

Find .

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Apply third derivative on each side with respect to .

.

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Apply fourth derivative on each side with respect to .

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Observe the sequence.

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.

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The  derivative of the function can be written as

.

.

.

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