&nbsp;f&nbsp;(&nbsp;x&nbsp;)&nbsp;=&nbsp;7&nbsp;x&nbsp;2&nbsp;+&nbsp;2&nbsp;and&nbsp;g&nbsp;(&nbsp;x&nbsp;)&nbsp;=&nbsp;5&nbsp;x&nbsp;3&nbsp;+&nbsp;7&nbsp;x&nbsp;2&nbsp;+&nbsp;6&nbsp;x, find the derivative of the quotient&nbsp;f&nbsp;(&nbsp;x&nbsp;)&nbsp;g&nbsp;(&nbsp;x&nbsp;)&nbsp;.

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&amp;nbsp;f&amp;nbsp;(&amp;nbsp;x&amp;nbsp;)&amp;nbsp;=&amp;nbsp;7&amp;nbsp;x&amp;nbsp;2&amp;nbsp;﻿+&amp;nbsp;2&amp;nbsp;and&amp;nbsp;g&amp;nbsp;(&amp;nbsp;x&amp;nbsp;)&amp;nbsp;=&amp;nbsp;5&amp;nbsp;x&amp;nbsp;3&amp;nbsp;+&amp;nbsp;7&amp;nbsp;x&amp;nbsp;2&amp;nbsp;+&amp;nbsp;6&amp;nbsp;x, find the derivative of the quotient&amp;nbsp;f&amp;nbsp;(&amp;nbsp;x&amp;nbsp;)&amp;nbsp;g&amp;nbsp;(&amp;nbsp;x&amp;nbsp;)&amp;nbsp;.

Elyse Huff · Accepted Answer

Set up the composite result function.g(f(x))Evaluate&amp;nbsp;g(7x2+2)&amp;nbsp;by substituting in the value of&amp;nbsp;f&amp;nbsp;into&amp;nbsp;g.g(7x2+2)=5(7x2+2)3+7(7x2+2)2+6(7x2+2)Simplify each term.g(7x2+2)=1715x6+1470x4+420x2+40+343x4+196x2+28+42x2+12Simplify by adding terms.g(7x2+2)=1715x6+1813x4+658x2+80

With f(x)=7x^{2}+2 f(x)=7x^{2}+2 Show External URL Show Embeded Code Hide MathML Code f(x)=

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