document.write( "Question 111639: Please help. I couldn't find any likes of a solution to this problem nor a section to enter this problem on the website :\r
\n" ); document.write( "\n" ); document.write( "Given that \"y=2%5Ex%2Ax%5E2\", prove that \"%28dy%29%2F%28dx%29+=%28y%282+%2B+x%2Aln%282%29%29%29%2Fx\". \n" ); document.write( "
Algebra.Com's Answer #81428 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Please help. I couldn't find any likes of a solution to this problem nor a section to enter this problem on the website :\r
\n" ); document.write( "\n" ); document.write( "Given that \"y=2%5Ex%2Ax%5E2\", prove that \"%28dy%29%2F%28dx%29+=%28y%282+%2B+x%2Aln%282%29%29%29%2Fx\".
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document.write( "\"y=2%5Ex%2Ax%5E2\"\r\n" );
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document.write( "take the \"1n\" of both sides:\r\n" );
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document.write( "\"ln%28y%29=ln%282%5Ex%2Ax%5E2%29\"\r\n" );
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document.write( "\"ln%28y%29=ln%282%5Ex%29+%2Bln%28x%5E2%29\"\r\n" );
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document.write( "\"ln%28y%29=x%2Aln%282%29+%2B2%2Aln%28x%29\"\r\n" );
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document.write( "Now, upon realizing that \"ln%282%29\" is just a constant,\r\n" );
document.write( "we can take the derivative of both sides:\r\n" );
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document.write( "\"%28%28dy%29%2F%28dx%29%29%2Fy=ln%282%29+%2B+2%2A%281%2Fx%29\"\r\n" );
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document.write( "or \r\n" );
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document.write( "\"%28%28dy%29%2F%28dx%29%29%2Fy=ln%282%29+%2B+2%2Fx\"\r\n" );
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document.write( "Clear of fractions by multiplying both sides by \"xy\":\r\n" );
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document.write( "\"xy%2A%28%28dy%29%2F%28dx%29%29%2Fy+=xy%2Aln%282%29+%2B+xy%2A%282%2Fx%29\"\r\n" );
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document.write( "Cancel the y's on the left, and cancel the x's in the\r\n" );
document.write( "rightmost term:\r\n" );
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document.write( "\"x%2A%28%28dy%29%2F%28dx%29%29+=xy%2Aln%282%29+%2B+2y\"\r\n" );
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document.write( "Factor out y on the right:\r\n" );
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document.write( "\"x%2A%28%28dy%29%2F%28dx%29%29+=y%28x%2Aln%282%29+%2B+2%29\"\r\n" );
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document.write( "Divide both sides by \"x\"\r\n" );
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document.write( "\"%28dy%29%2F%28dx%29+=%28y%28x%2Aln%282%29+%2B+2%29%29%2Fx\"\r\n" );
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document.write( "Reverse the two terms in the parentheses:\r\n" );
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document.write( "\"%28dy%29%2F%28dx%29+=%28y%282+%2B+x%2Aln%282%29%29%29%2Fx\"\r\n" );
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document.write( "Edwin
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