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if x^2+y^2 = t - 1/t and x^4 + y^4 = t^2...

if `x^2+y^2 = t - 1/t` and` x^4 + y^4 = t^2 + 1/t^2 `then prove that `dy/dx = 1/(x^3y)`

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Given `x^2 + y^2 = t + 1/t`
`x^4 + y^4 = t^2 + 1/t^2` ……(i)
`(x^2 + y^2)^2 = (t + 1/t )^2`
`x^4 + y^4 + 2x^2y^2= t^2 +1/t^2 + 2`
...
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