SOLUTION: could you please find the derivatives of the function given by: y=((2/x^2)+x)^-1/3 please show all working

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Question 328340: could you please find the derivatives of the function given by:
y=((2/x^2)+x)^-1/3
please show all working
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the chain rule.
Let u=%282%2Fx%5E2%29%2Bx+=2x%5E%28-2%29%2Bx
y=u%5E%28-1%2F3%29
dy%2Fdx=%28dy%2Fdu%29%28du%2Fdx%29
dy%2Fdu=%28-1%2F3%29u%5E%28-%281%2F3%29-1%29=-%281%2F3%29u%5E%28-4%2F3%29
du%2Fdx=-4x%5E%28-3%29%2B1
Put it all together,
dy%2Fdx=-%281%2F3%29u%5E%28-4%2F3%29%2A%28-4x%5E%28-3%29%2B1%29
dy%2Fdx=%284%2Fx%5E3-1%29%2F3u%5E%284%2F3%29
dy%2Fdx=%284%2Fx%5E3-1%29%2F3%28%282%2Fx%5E2%29%2Bx+%29%5E%284%2F3%29