To find the derivative of the function F$x$ = √x + x^2 + 1/x - 1, we need to differentiate each term separately using the rules of differentiation.

Differentiate √x:
The derivative of √x is $1/2$ * x^$-1/2$

Differentiate x^2:
The derivative of x^2 is 2x

Differentiate 1/x:
The derivative of 1/x is -1/x^2

Differentiate the constant term -1:
The derivative of a constant term is zero.

Now, putting it all together, the derivative of F$x$ is:
F'$x$ = $1/2$ * x^$-1/2$ + 2x - 1/x^2

Simplified, the derivative is:
F'$x$ = 1/$2\surd x$ + 2x - 1/x^2