If y = x2 - (1/x). find dy/dx

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).