2. Let u,v be functions of x. The first order derivative of uv can be derived by the following product rule: (uv)⁰ = uºv + uvo. The general n-th order derivative of uv, called the general Leibniz rule, was obtained by the German mathematician Gottfried Wilhelm Leibniz: where (2) = Ch = (uv) (n) = [ - Σ (2) ² k=0 n! k!(n − k)!. u(k) y(n-k) (a) Verify the general Leibniz's rule when n = 1,2,3. (b) Find f(1510)(x) if f(x) = (x² + x) sin(2x)
2. Let u,v be functions of x. The first order derivative of uv can be derived by the following product rule: (uv)⁰ = uºv + uvo. The general n-th order derivative of uv, called the general Leibniz rule, was obtained by the German mathematician Gottfried Wilhelm Leibniz: where (2) = Ch = (uv) (n) = [ - Σ (2) ² k=0 n! k!(n − k)!. u(k) y(n-k) (a) Verify the general Leibniz's rule when n = 1,2,3. (b) Find f(1510)(x) if f(x) = (x² + x) sin(2x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Let u,v be functions of x. The first order derivative of uv can be derived by the
following product rule:
(uv)⁰ = uºv + uvº.
The general n-th order derivative of uv, called the general Leibniz rule, was
obtained by the German mathematician Gottfried Wilhelm Leibniz:
where
(2)
CK
n
(uv)
(re)(n) = (17.) ()
k=0
n!
k!(n − k)!.
u(k) y(n-k)
(a) Verify the general Leibniz's rule when n= 1,2,3.
(b) Find f(1510)(x) if
f(x) = (x² + x)sin(2x)
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