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w(t) = cos(3t) cos(7t)

Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill ISBN: 9781111427412 173

Solution for problem 3.4 Chapter 3

Advanced Engineering Mathematics | 7th Edition

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Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill

Advanced Engineering Mathematics | 7th Edition

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Problem 3.4

w(t) = cos(3t) cos(7t)

Step-by-Step Solution:
Step 1 of 3

Overview week of 9/12/16 3.3 Rules of Differentiation Power of X: d n (n­1) Power Rule: / Xdx= nX Quotient Rule: / f(x)/g(x) = [(f(x) * g(x)) – (f(x) * g(x))] / [g(x)] 2 dx Product Rule: / [dxx) * g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Chain Rule: / [dxg(x))] = [f(g(x))]’ * g’(x) Constant Multiple: Power rule d /dx(cf(x)) = c * f ’(x) 3.4 Product and Quotient Rules Product Rule: While [f(x) +/­ g(x)]’ = f ‘(x) +/­ g’(x), The same does not apply to multiplication And division. [f(x)g(x)] ≠ f ‘(x) * g’(x) Instead: [f(x)g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Products of multiple functions: (fg)’ = f’g + fg’ (fgh)’ = f’gh + fg’h + fgh’ (fghi)’ = f’ghi + fg’hi + fgh’i + fghi’

Step 2 of 3

Chapter 3, Problem 3.4 is Solved
Step 3 of 3

Textbook: Advanced Engineering Mathematics
Edition: 7
Author: Peter V. O'Neill
ISBN: 9781111427412

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w(t) = cos(3t) cos(7t)