If y = x2 - $\frac{1}{x}$, find $\frac{\delta y}{\delta x}$

Analyze the question: We need the derivative of y = x² − 1/x with respect to x. (The "x2" is read as x².)

Concept: Use the power rule: d/dx (xⁿ) = n·xⁿ⁻¹. First rewrite 1/x as x⁻¹.

Solution:

1. Rewrite the function: y = x² − x⁻¹

2. Differentiate each term: • d/dx (x²) = 2x • d/dx (−x⁻¹) = −(−1)x⁻² = +x⁻² = 1/x²

3. Combine: dy/dx = 2x + 1/x²

Check against the options:

• A. 2x − 1/x²: wrong sign on the second term.
• B. 2x + x²: the second term is wrong.
• C. 2x − x²: wrong.
• D. 2x + 1/x²: matches my working.

Tip: Always convert fractions like 1/xⁿ into x⁻ⁿ before differentiating. Watch the signs: a minus in front of x⁻¹ combined with the power −1 gives a plus, so the derivative of −1/x is +1/x².