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Get Full Access to Single Variable Calculus - 7 Edition - Chapter 5 - Problem 27
Get Full Access to Single Variable Calculus - 7 Edition - Chapter 5 - Problem 27

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# A force of 30 N is required to maintain a spring | Ch 5 - 27 ISBN: 9780538497831 151

## Solution for problem 27 Chapter 5

Single Variable Calculus | 7th Edition

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Problem 27

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?

Step-by-Step Solution:
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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’

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##### ISBN: 9780538497831

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