d/dx [x*x^1/2(x - 1/x)^2]

I know that i'm supposed to simply this equation, but I don't know where to stop to take the derivative.

Here are my simplification steps:

f(x) = x*x^1/2(x - 1/x)^2

f(x) = x^(3/2) (x-1/x)^2

f(x) = x^(3/2) (x + x^(-1))^2 -> Quick side note question: When taking the reciprocal does the sign change?

f(x) = x^(3/2) (x^2 + 2 + x^-2)

f(x) = x^(7/2) + 2x^(3/2) + x^(-1/2)

d/dx = 7/2x^(5/2) + 3x^(1/2) -1/2x^(1/2)

Where did I go wrong?