document.write( "Question 1193108: Use the logarithmic differentiation to differentiate the function
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Algebra.Com's Answer #825360 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"%0D%0Aroot%283%2C%28x%5E4%28x%5E%22%22-2%29%29%2F%28%28x%5E2-2%29%282x%5E%22%22%2B3%29%29%29\"\r\n" );
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document.write( "Change the root to an fractional exponential\r\n" );
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Take natural logs of both sides:\r\n" );
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document.write( "\"ln%28f%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Use the property of logarithms that allows us to\r\n" );
document.write( "move the exponent (1/3) in front of the ln.\r\n" );
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document.write( "\"ln%28f%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Clear the fraction by multiplying both sides by 3\r\n" );
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document.write( "\"3%2Aln%28f%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\"ln%28%0D%0A%28x%5E4%28x%5E%22%22-2%29%29%2F%28%28x%5E2-2%29%282x%5E%22%22%2B3%29%29%29\"\r\n" );
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document.write( "On the right side, write the log of a quotient as \r\n" );
document.write( "the log of the numerator minus the log of the \r\n" );
document.write( "denominator.\r\n" );
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document.write( "\"3%2Aln%28f%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "On the right side, use the fact that the log of\r\n" );
document.write( "a product is the sum of the logs: \r\n" );
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document.write( "\"3%2Aln%28f%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "On the right side write the 4 exponent in front of the log. \r\n" );
document.write( "Remove the largest parentheses:\r\n" );
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document.write( "\"3%2Aln%28f%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\"4%2Aln%28x%5E%22%22%29%2Bln%28x-2%5E%22%22%29-ln%28x%5E2-2%29-ln%282x%2B3%5E%22%22%29\"\r\n" );
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document.write( "Take the derivative of both sides, using:\r\n" );
document.write( "The derivative of a natural log of an expression\r\n" );
document.write( "is the derivative of the expression divided by\r\n" );
document.write( "the expression:\r\n" );
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document.write( "\"3%2Aexpr%28%22f%27%28x%29%22%2Ff%28x%29%29%29\"\"%22%22=%22%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "Put the 4 in the numerator in the first term on the right:\r\n" );
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document.write( "\"3%2Aexpr%28%22f%27%28x%29%22%2Ff%28x%29%29%29\"\"%22%22=%22%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "Divide both sides by 3:\r\n" );
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document.write( "\"expr%28%22f%27%28x%29%22%2Ff%28x%29%29%29\"\"%22%22=%22%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "Multiply both sides by f(x)\r\n" );
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document.write( "\"%22f%27%28x%29%22\"\"%22%22=%22%22\"\"%22%22=%22%22\"\r\n" );
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document.write( "Substitute for f(x) from the original equation\r\n" );
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document.write( "\"%22f%27%28x%29%22\"\"%22%22=%22%22\"\"%22%22=%22%22\"\r\n" );
document.write( "  \r\n" );
document.write( "Edwin
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