document.write( "Question 168880: What is the derivative of this function.?If y= x^2 - 4x and x = sqrt of 2t^2 +1 find dy/dt when t = sqrt of 2. \n" ); document.write( "

Algebra.Com's Answer #124579 by Fombitz(32388) $\"\"$ $\"About$

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By the chain rule,
\n" ); document.write( " $\"dy%2Fdt=%28dy%2Fdx%29%2A%28dx%2Fdt%29\"$
\n" ); document.write( " $\"dy%2Fdx=2x-4\"$
\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( " $\"dy%2Fdt=%28dy%2Fdx%29%2A%28dx%2Fdt%29\"$
\n" ); document.write( " $\"dy%2Fdt=%282x-4%29%2A%28%282t%29%2F%28sqrt%282t%5E2%2B1%29%29%29\"$
\n" ); document.write( " $\"dy%2Fdt=%282%2Asqrt%282t%5E2%2B1%29-4%29%2A%28%282t%29%2F%28sqrt%282t%5E2%2B1%29%29%29\"$
\n" ); document.write( "When $\"t=sqrt%282%29\"$ , then
\n" ); document.write( " $\"t%5E2=2\"$
\n" ); document.write( "

\n" ); document.write( " $\"dy%2Fdt=%282%2Asqrt%285%29-4%29%2A%28%282%2Asqrt%282%29%29%2F%28sqrt%285%29%29%29\"$
\n" ); document.write( " $\"dy%2Fdt=%284%2Asqrt%282%29%28sqrt%285%29-2%29%29%2F%28sqrt%285%29%29\"$ \n" ); document.write( "

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