document.write( "Question 200580: Hi all, Can someone please show me, with working; how to differentiate the following with respect to x.
\n" ); document.write( "These are three seperate equations with seperate answers.
\n" ); document.write( "1. \"y=3x%5E2+%2B+4x+%2B+2\"\r
\n" ); document.write( "\n" ); document.write( "2. \"y=x%5E2%2Asqrt%28x%29+%2B+1%2Fsqrt%28x%29+-+cos%283x%29\"\r
\n" ); document.write( "\n" ); document.write( "3. \"y=e%5E3x+%28x%5E2+%2B+ln%28x%29%29\"
\n" ); document.write( "If someone could show me one or all 3 that would be great.
\n" ); document.write( "Thanks, -nick.
\n" ); document.write( "

Algebra.Com's Answer #150844 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "From algebra, you need to know that \r\n" );
document.write( "1. \"sqrt%28u%29=u%5E%281%2F2%29\" \r\n" );
document.write( "2. \"1%2F%28u%5En%29+=+u%5E%28-n%29\"\r\n" );
document.write( "and from calculus you need to know that\r\n" );
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document.write( "3. For \"y=u%5En\", then \"%28dy%29%2F%28dx%29=n%2Au%5E%28n-1%29%28%28du%29%2F%28dx%29%29\"\r\n" );
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document.write( "4. For \"y=cos%28u%29\", then \"+%28dy%29%2F%28dx%29+=+-sin%28u%29%28%28du%29%2F%28dx%29%29\"\r\n" );
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document.write( "5. For \"y=e%5Eu\", then \"%28dy%29%2F%28dx%29=%28e%5Eu%29%28%28du%29%2F%28dx%29%29\"\r\n" );
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document.write( "6. For \"y=ln%28u%29\", then \"%28dy%29%2F%28dx%29=%28%28du%29%2F%28dx%29%29%2Fu\"\r\n" );
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document.write( "7. For \"y=u%2Av\", then \"%28dy%29%2F%28dx%29=u%28%28dv%29%2F%28dx%29%29%2Bv%28%28du%29%2F%28dx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1. \"y=3x%5E2+%2B+4x+%2B+2\"\r\n" );
document.write( "   \"%28dy%29%2F%28dx%29=6x%2B4\" \r\n" );
document.write( "\r\n" );
document.write( "2. \"y=x%5E2%2Asqrt%28x%29+%2B+1%2Fsqrt%28x%29+-+cos%283x%29\"\r\n" );
document.write( "   \"y=%28x%5E2%29%28x%5E%281%2F2%29%29+%2B+1%2F%28x%5E%281%2F2%29%29+-+cos%283x%29\"\r\n" );
document.write( "   \"y=x%5E%282%2B1%2F2%29%2Bx%5E%28-1%2F2%29-cos%283x%29\"\r\n" );
document.write( "   \"y=x%5E%285%2F2%29%2Bx%5E%28-1%2F2%29-cos%283x%29\"\r\n" );
document.write( "   \r\n" );
document.write( "   \"%28dy%29%2F%28dx%29=%285%2F2%29x%5E%283%2F2%29-%281%2F2%29x%5E%28-3%2F2%29%2B3sin%283x%29\"\r\n" );
document.write( "\r\n" );
document.write( "3. \"y=e%5E%283x%29+%28x%5E2+%2B+ln%28x%29%29\"\r\n" );
document.write( "    \r\n" );
document.write( "   \"%28dy%29%2F%28dx%29=e%5E%283x%29%282x%2B1%2Fx%29%2B3e%5E%283x%29%28x%5E2%2Bln%28x%29%29\"\r\n" );
document.write( "   \"%28dy%29%2F%28dx%29=e%5E%283x%29%28%282x%2B1%2Fx%29%2B3%28x%5E2%2Bln%28x%29%29%29\"\r\n" );
document.write( "   \"%28dy%29%2F%28dx%29=e%5E%283x%29%282x%2B1%2Fx%2B3x%5E2%2B3%2Aln%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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