document.write( "Question 328340: could you please find the derivatives of the function given by:\r
\n" ); document.write( "\n" ); document.write( "y=((2/x^2)+x)^-1/3\r
\n" ); document.write( "\n" ); document.write( "please show all working \n" ); document.write( "

Algebra.Com's Answer #235224 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the chain rule.
\n" ); document.write( "Let $\"u=%282%2Fx%5E2%29%2Bx+=2x%5E%28-2%29%2Bx\"$
\n" ); document.write( " $\"y=u%5E%28-1%2F3%29\"$
\n" ); document.write( " $\"dy%2Fdx=%28dy%2Fdu%29%28du%2Fdx%29\"$
\n" ); document.write( " $\"dy%2Fdu=%28-1%2F3%29u%5E%28-%281%2F3%29-1%29=-%281%2F3%29u%5E%28-4%2F3%29\"$
\n" ); document.write( " $\"du%2Fdx=-4x%5E%28-3%29%2B1\"$
\n" ); document.write( "Put it all together,
\n" ); document.write( " $\"dy%2Fdx=-%281%2F3%29u%5E%28-4%2F3%29%2A%28-4x%5E%28-3%29%2B1%29\"$
\n" ); document.write( " $\"dy%2Fdx=%284%2Fx%5E3-1%29%2F3u%5E%284%2F3%29\"$
\n" ); document.write( " $\"dy%2Fdx=%284%2Fx%5E3-1%29%2F3%28%282%2Fx%5E2%29%2Bx+%29%5E%284%2F3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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