document.write( "Question 1082781: Derivative of 2^x^2=.......... \n" ); document.write( "
Algebra.Com's Answer #696854 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There is no way to tell whether 2^x^2 means \"matrix%282%2C1%2C%22%22%2C2%5E%28%28x%5E2%29%29%29\" or \"%282%5Ex%29%5E2\".\r\n" );
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document.write( "That's why it is necessary to use parentheses when typing algebra \r\n" );
document.write( "containing exponents or denominators all on one line.\r\n" );
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document.write( "If you mean the derivative of \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Cy+=2%5E%28%28x%5E2%29%29%29\"\r\n" );
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document.write( "We take natural logarithms of both sides\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Cln%28y%29+=ln%282%5E%28%28x%5E2%29%29%29%29\"\r\n" );
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document.write( "Then use a rule of logarithms:\r\n" );
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document.write( "\"ln%28y%29+=x%5E2%2Aln%282%29\"\r\n" );
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document.write( "[Note: ln(2) is just a constant.]\r\n" );
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document.write( "\"%22y%27%22%2Fy=2x%2Aln%282%29\"\r\n" );
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document.write( "\"%22y%27%22=y%2A2x%2Aln%282%29\"\r\n" );
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document.write( "Replace y by \"matrix%282%2C1%2C%22%22%2C2%5E%28%28x%5E2%29%29%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22y%27%22=2%5E%28%28x%5E2%29%29%2A2x%2Aln%282%29%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22y%27%22=2%5E%28%28x%5E2%29%29%2A2%5E1%2Ax%2Aln%282%29%29\"\r\n" );
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document.write( "Add exponents of 2\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22y%27%22=2%5E%28%28x%5E2%2B1%29%29%2Ax%2Aln%282%29%29\"\r\n" );
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document.write( "If you mean the derivative of \r\n" );
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document.write( "\"y=%282%5Ex%29%5E2\"\r\n" );
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document.write( "Multiply exponents:\r\n" );
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document.write( "\"y=2%5E%282x%29\"\r\n" );
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document.write( "We take natural logarithms of both sides\r\n" );
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document.write( "\"ln%28y%29+=ln%282%5E%282x%29%29\"\r\n" );
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document.write( "Use a rule of logarithms:\r\n" );
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document.write( "\"ln%28y%29+=2x%2Aln%282%29\"\r\n" );
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document.write( "[Note: ln(2) is just a constant.  \r\n" );
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document.write( "\"%22y%27%22%2Fy=2%2Aln%282%29\"\r\n" );
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document.write( "\"%22y%27%22=y%2A2%2Aln%282%29\"\r\n" );
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document.write( "Replace y by \"2%5E%282x%29\"\r\n" );
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document.write( "\"%22y%27%22=2%5E%282x%29%2A2%2Aln%282%29\"\r\n" );
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document.write( "\"%22y%27%22=2%5E%282x%29%2A2%5E1%2Aln%282%29\"\r\n" );
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document.write( "Add exponents of 2\r\n" );
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document.write( "\"%22y%27%22=2%5E%282x%2B1%29%2Aln%282%29\"\r\n" );
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document.write( "Edwin
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