I'm assuming you want me to explain how to find the derivative of each of these functions.

1) To find the derivative of y = x^2 - x + 1/x^2 + x + 1, you need to differentiate each term separately. The derivative of x^2 is 2x, the derivative of -x is -1, and the derivative of 1/x^2 can be found using the power rule for differentiation: -2/x^3. The derivative of x is 1 and the derivative of 1 is 0. Putting it all together, the derivative of the function is:

y' = 2x - 1 - 2/x^3 + 1

2) To find the derivative of y = ln(√(2x) - 1), you need to use the chain rule for differentiation. Let u = √(2x) - 1, then y = ln(u). The derivative of ln(u) is 1/u times the derivative of u.

First, find the derivative of u:

u' = 1/2 * (2x)^(-1/2) = 1/(2√(2x))

Then, apply the chain rule to find the derivative of y:

y' = (1/u) u' = (1/(√(2x) - 1)) (1/(2√(2x)))

Simplifying that, the derivative becomes:

y' = 1/(2(√(2x)(√(2x) - 1))

These are the derivatives of the two functions you provided. Let me know if you have any questions or need further explanation.