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LEIBNITZ'S THEOREM, If and are functions of, such that their, of their product is given by, , where, , and, , Example11, , represent, Find the, , Solution: Let, , derivatives of, , derivative of, and, , and, , Then, , theorem, we have, , Example 12 Find the, Solution: Let, , derivative of, and, , Then, , theorem, we have, , derivatives exist, then the, , and, , respectively., , derivative

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Example 13, , If, , , show that, =0, , Solution:, , Here, , Example 14, , If, , Prove that, , )

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Example 15 If, , , show that, ..., , Putting, , in the above equation, we get

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Example 16 If, , show that, , and, , we get, , Putting, , in the above equation, we get

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Example 17 If, , , show that, , and, , we get, , Putting, , in the above equation, we get, , we get

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Example18, , If, , show that, , and, , we get

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we get, , Putting, , in the above equation, we get, , Exercise 1 B, 1 .Find, , 2. Find, , If, , If, , If, , ), prove that, , show that, , , show that