3. The Leibniz rule for the nth derivative of a product is given by dn dx" n (f(x) g(x)) = f(")(x)g(x) + 7+ f("-¹)(x)g '(x) 1! n(n − 1) fƒ(n-2)(x)g(²)(x) + + 2! where the coefficients are the same as the coefficients in the binomial expansion. n(n − 1) 2! An-3 B³+ + B". n (A + B)" = A" + " A"¯¹ B + ... + n(n-1)(n-2) 3! Use mathematical induction to establish the Leibniz rule. + f(x) g(n)(x), An-2B²

3. The Leibniz rule for the nth derivative of a product is given by dn dx" n (f(x) g(x)) = f(")(x)g(x) + 7+ f("-¹)(x)g '(x) 1! n(n − 1) fƒ(n-2)(x)g(²)(x) + + 2! where the coefficients are the same as the coefficients in the binomial expansion. n(n − 1) 2! An-3 B³+ + B". n (A + B)" = A" + " A"¯¹ B + ... + n(n-1)(n-2) 3! Use mathematical induction to establish the Leibniz rule. + f(x) g(n)(x), An-2B²

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.

Chapter3: The Derivative

Section3.3: Rates Of Change

Problem 30E: If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing...

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