document.write( "Question 389719: if x^2 -y^2=5 what is d^2y/dx^2 at the point (3,2) \n" ); document.write( "
Algebra.Com's Answer #276281 by richard1234(7193)\"\" \"About 
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\"x%5E2+-+y%5E2+=+5\"\r
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\n" ); document.write( "\n" ); document.write( "Differentiating with respect to x,\r
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\n" ); document.write( "\n" ); document.write( "\"2x+-+2y%28dy%2Fdx%29+=+0\" Isolate dy/dx\r
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\n" ); document.write( "\n" ); document.write( "\"dy%2Fdx+=+-2x%2F-2y+=+x%2Fy\"\r
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\n" ); document.write( "\n" ); document.write( "Take the second derivative \"d%5E2y%2Fdx%5E2\" using the Quotient rule:\r
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\n" ); document.write( "\n" ); document.write( "\"d%5E2y%2Fdx%5E2+=+%28y+-+x%28dy%2Fdx%29%29%2F%28y%5E2%29\"\r
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\n" ); document.write( "\n" ); document.write( "Replace \"dy%2Fdx\" with \"x%2Fy\"\r
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\n" ); document.write( "\n" ); document.write( "\"d%5E2y%2Fdx%5E2+=+%28y+-+x%5E2%2Fy%29%2Fy%5E2+=+1%2Fy+-+x%5E2%2Fy%5E3\" (splitting up the fraction and simplifying)\r
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\n" ); document.write( "\n" ); document.write( "Replacing x = 3 and y = 2, \"d%5E2y%2Fdx%5E2\" at the point (3,2) is \"1%2F2+-+9%2F8+=+-5%2F8\"
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