34 Prove the Leibniz rule for the nth derivative of the product of two n times dierentiable functions as given in (9 42) Namely, if hx f xgx, then hnx Xn k0 n k f kxgnkx where f 0x1 f x, and similarly g0x1gx (Hint Use mathematical induction ) ...

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34. Prove the Leibniz rule for the nth-derivative of the product of two n-times dierentiable functions as

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34. Prove the Leibniz rule for the nth-derivative of the product of two n-times di¤erentiable functions as given in (9.42). Namely, if hðxÞ ¼ f ðxÞgðxÞ, then hðnÞðxÞ ¼

Xn k¼0 n

k f ðkÞðxÞgðnkÞðxÞ;

where f ð0ÞðxÞ1 f ðxÞ, and similarly gð0ÞðxÞ1gðxÞ. (Hint: Use mathematical induction.)

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Introduction To Quantitative Finance A Math Tool Kit

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34. Prove the Leibniz rule for the nth-derivative of the product of two n-times dierentiable functions as

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Introduction To Quantitative Finance A Math Tool Kit

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