document.write( "Question 840705: 1. Differentiate f(x) = {square-root of [(x-1) divided by (x+1)]}.
\n" ); document.write( "2. Differentiate (2y-x)^6 + x^3 = y = 3.
\n" ); document.write( "3. Evaluate the derivatives of the function at the point
\n" ); document.write( " 3x^3y^2 - 2y3 = -3; (1,2). thank you so much.
\n" ); document.write( "

Algebra.Com's Answer #509937 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "1. Differentiate f(x) = {square-root of [(x-1) divided by (x+1)]}.
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document.write( "\"f%28x%29\"\"%22%22=%22%22\"\"sqrt%28%28x-1%29%2F%28x%2B1%29%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Cf%28x%29%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\"matrix%282%2C1%2C%22%22%2C%28%28x-1%29%2F%28x%2B1%29%29%5E%281%2F2%29%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%27%28x%29%22\"\"%22%22=%22%22\"\"sqrt%28%28x%2B1%29%2F%28x-1%29%29%28expr%281%2F%28x%2B1%29%5E2%29%29\"\r\n" );
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\n" ); document.write( "2. Differentiate (2y-x)^6 + x^3 = y = 3.
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document.write( "I'll assume that last equal sign was a typo and should be a +,\r\n" );
document.write( "and that you meant\r\n" );
document.write( "

\n" ); document.write( "2. Differentiate (2y-x)^6 + x^3 = y + 3.
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document.write( "\"%282y-x%29%5E6+%2B+x%5E3\"\"%22%22=%22%22\"\"y+%2B+3\"\r\n" );
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document.write( "\"6%282y-x%29%5E5%282%2Aexpr%28dy%2Fdx%29-1%29%2B3x%5E2\"\"%22%22=%22%22\"\"dy%2Fdx%2B0\"\r\n" );
document.write( "\r\n" );
document.write( "\"12%282y-x%29%5E5%2Aexpr%28dy%2Fdx%29%2B18x%5E2%282y-x%29%5E5\"\"%22%22=%22%22\"\"dy%2Fdx\"\r\n" );
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document.write( "Solve for \"dy%2Fdx\"\r\n" );
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document.write( "\"12%282y-x%29%5E5%2Aexpr%28dy%2Fdx%29\"\"%22%22-%22%22\"\"dy%2Fdx\" \"%22%22=%22%22\" \"-18x%5E2%282y-x%29%5E5\"\r\n" );
document.write( "\r\n" );
document.write( "\"%2812%282y-x%29%5E5-1%29expr%28dy%2Fdx%29\"\"%22%22=%22%22\"\"-18x%5E2%282y-x%29%5E5\"\r\n" );
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document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\"%28-18x%5E2%282y-x%29%5E5%29%2F%2812%282y-x%29%5E5-1%29\"\r\n" );
document.write( "

\n" ); document.write( "3. Evaluate the derivatives of the function at the point
\n" ); document.write( " 3x^3y^2 - 2y3 = -3; (1,2). thank you so much.
\n" ); document.write( "
\r\n" );
document.write( "\"3x%5E3y%5E2+-+2y%5E3\"\"%22%22=%22%22\"\"-3\"\r\n" );
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document.write( "\"%283x%5E3%2A2y%2Aexpr%28dy%2Fdx%29%2By%5E2%2Ax%5E2%29-6y%5E2%2Aexpr%28dy%2Fdx%29\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"6x%5E3y%2Aexpr%28dy%2Fdx%29%2By%5E2%2Ax%5E2-6y%5E2%2Aexpr%28dy%2Fdx%29\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
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document.write( "Solve for \"dy%2Fdx\"\r\n" );
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document.write( "\"6x%5E3y%2Aexpr%28dy%2Fdx%29-6y%5E2%2Aexpr%28dy%2Fdx%29\"\"%22%22=%22%22\"\"-y%5E2%2Ax%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"%286x%5E3y-6y%5E2%29%2Aexpr%28dy%2Fdx%29\"\"%22%22=%22%22\"\"-y%5E2%2Ax%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"6y%28x%5E3-y%29%2Aexpr%28dy%2Fdx%29\"\"%22%22=%22%22\"\"-y%5E2%2Ax%5E2\"\r\n" );
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document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\"%28-y%5E2%2Ax%5E2%29%2F%286y%28x%5E3-y%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\"%28-y%5Ecross%282%29%2Ax%5E2%29%2F%286cross%28y%29%28x%5E3-y%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"dy%2Fdx\"\"%22%22=%22%22\"\"%28-y%2Ax%5E2%29%2F%286%28x%5E3-y%29%29\"\r\n" );
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document.write( "Substitute (x,y) = (1,2).\r\n" );
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document.write( "\"%28dy%2Fdx%29%5B%22%281%2C2%29%22%5D\" \"%22%22=%22%22\"\"%28-2%2A1%5E2%29%2F%286%281%5E3-2%29%29\"\"%22%22=%22%22\"\"%28-2%29%2F%286%281-2%29%29\"\"%22%22=%22%22\"\"%28-2%29%2F%286%2A%28-1%29%29\"\"%22%22=%22%22\"\"%28-2%29%2F%28-6%29\"\"%22%22=%22%22\"\"1%2F3\"\r\n" );
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document.write( "Edwin
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