If \(y = x^2 - \frac{1}{x}\), find \(\frac{\delta y}{\delta x}\)

To find δyδx (the derivative of y with respect to x), we need to apply the power rule of differentiation, which states that if y = x^n, then δyδx = n*x^(n-1). Applying this rule to y = x^2 - 1/x, we get: δyδx = 2x + 1/x^2 Therefore, the answer is not one of the options provided. Option A (2x - 1/x^2) is close but has a minus sign instead of a plus sign before the second term. Option B (2x + x^2) and option C (2x - x^2) are incorrect because they don't take into account the derivative of the second term (-1/x). Option D (2x + 1/x^2) is the correct answer based on the power rule of differentiation.