Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following generalization of the product rule: n dn - (f(x)g(x)) = [ (1) f(k) (x) g(n-k) (x) . dxn k k=0
Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following generalization of the product rule: n dn - (f(x)g(x)) = [ (1) f(k) (x) g(n-k) (x) . dxn k k=0
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 36E
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