document.write( "Question 163503: Differentiate with respect to x,\r
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Algebra.Com's Answer #120909 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Differentiate with respect to x,
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document.write( "a) \"y=%282x%29%2F%28e%5Ex%29\"\r\n" );
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document.write( "Write with constant coefficient \"2\" outside\r\n" );
document.write( "   \"y=2%28x%2Fe%5Ex%29\"\r\n" );
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document.write( "Write denominator as a factor of numerator with negative\r\n" );
document.write( "exponent:\r\n" );
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document.write( "   \"y=2%28x%2Ae%5E%28-x%29%29\"\r\n" );
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document.write( "Use product rules for derivative \"d%28u%2Av%29%2Fdx=u%28dv%2Fdx%29%2Bv%28du%2Fdx%29\"\r\n" );
document.write( "and \"d%28e%5Eu%29%2Fdx=%28e%5Eu%29%28du%2Fdx%29\"\r\n" );
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document.write( "of the inside of parentheses:\r\n" );
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document.write( "   \"dy%2Fdx=2%28x%2Ae%5E%28-x%29%2A%28-1%29%2Be%5E%28-x%29%2A%281%29%29\"  \r\n" );
document.write( "   \"dy%2Fdx=2%28-x%2Ae%5E%28-x%29%2Be%5E%28-x%29%29\" \r\n" );
document.write( "factor out \"e%5E%28-x%29\"\r\n" );
document.write( "   \"dy%2Fdx=2%28e%5E%28-x%29%28-x%2B1%29%29\"\r\n" );
document.write( "   \"dy%2Fdx=2%28e%5E%28-x%29%281-x%29%29\"\r\n" );
document.write( "Write \"e%5E%28-x%29\" in the numerator as \"e%5Ex\" in the denominator\r\n" );
document.write( "   \"dy%2Fdx=%282%281-x%29%29%2F%28e%5Ex%29\"\r\n" );
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document.write( "---------------------\r\n" );
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document.write( "b) \"y=3x%2Asin%282x%29\"\r\n" );
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document.write( "Write with constant coefficient \"3\" outside\r\n" );
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document.write( "   \"y=3%28x%2Asin%282x%29%29\"\r\n" );
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document.write( "Use product rule for derivative \"d%28u%2Av%29%2Fdx=u%28dv%2Fdx%29%2Bv%28du%2Fdx%29\"\r\n" );
document.write( "and \"d%28sin%28u%29%29%2Fdx=cos%28u%29%28du%2Fdx%29\"\r\n" );
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document.write( "of the inside of parentheses:\r\n" );
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document.write( "  \"dy%2Fdx=3%28x%2Acos%282x%29%2A%282%29%2Bsin%282x%29%2A%281%29%29\" \r\n" );
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document.write( "  \"dy%2Fdx=3%282x%2Acos%282x%29%2Bsin%282x%29%29\"\r\n" );
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document.write( "Edwin
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