One of several Leibniz Rules in calculus deals with higher-order derivatives of products. Let (fg) (n) denote
Question:
One of several Leibniz Rules in calculus deals with higher-order derivatives of products. Let (fg)(n) denote the nth derivative of the product fg, for n ≥ 1.
a. Prove that (fg)(2) = f"g + 2 f'g' + fg".
b. Prove that, in general,
whereare the binomial coefficients.
c. Compare the result of (b) to the expansion of (a + b)n.
Transcribed Image Text:
п п f(k)g(n=k). |(f8)(") Σ k=0 п п! k) k.(п — К)!
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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