To find dy/dx, we need to differentiate y with respect to x using the rules of differentiation.
Let's start by expressing y in terms of x:
y = x^2 - (1/x)
To differentiate this expression, we need to use the power rule and the quotient rule.
The power rule states that if y = x^n, then dy/dx = nx^(n-1).
The quotient rule states that if y = u/v, then dy/dx = (v du/dx - u dv/dx) / v^2.
Using the power rule, we can find the derivative of x^2:
d/dx (x^2) = 2x
Using the quotient rule, we can find the derivative of (1/x):
d/dx (1/x) = -1/x^2
Now we can use these results to find the derivative of y:
dy/dx = d/dx (x^2) - d/dx (1/x)
= 2x - (-1/x^2)
= 2x + 1/x^2
Therefore, the answer is option D: 2x + (1/x^2).