Use Leibnizs theorem (Question 71) to find the following Data from Question 71 If y u(x)v(x), prove that Hence prove Leibnizs theorem for the nth derivative of a product (a) d dxs (x sin x) (put u sin x, v x) d dx(3x 1) (b) (re ) d4 d x4...

Use Leibnizs theorem (Question 71) to find the following: Data from Question 71 If y = u(x)v(x),

Question:

Use Leibniz’s theorem (Question 71) to find the following:

(a) d dxs (x sin x) (put u = sinx, v = x) d dx(3x + 1)] (b) (re ) d4 d.x4

Data from Question 71

If y = u(x)v(x), prove that

(a) y(x) = u(x)v(x) + 2u(x)v(x) + u(x)v)(x) (b) y(x) = u(x)v(x) + 3u2(x)v(x) + 3u(x)v(x) + u(x)v(x)

Hence prove Leibniz’s theorem for the nth derivative of a product:

n y")(x) = u"(x)v(x) + (1) (-2)(x) n +(2) -u) (n-1)(x)v()(x) 1-)(x)v()(x) + ... + u(x)v")(x)

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Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

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Question Posted: Jan 13, 2024 09:06 AM

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Use Leibnizs theorem (Question 71) to find the following: Data from Question 71 If y = u(x)v(x),

Question:

(a) d dxs (x sin x) (put u = sin .x, v = x) d dx(3x + 1)] (b) (re ) d4 d.x4

Step by Step Answer:

a b c d x sinx sin x3...View the full answer

Modern Engineering Mathematics

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