Question

If \( y = x(x - 1)(x - 2) \), then the derivative \( \frac{dy}{dx} \) is

• A. \( 3x^2 - 6x - 2 \)
• B. \( 3x^2 - 6x + 2 \)
• C. \( 3x^2 + 6x + 2 \)
• D. \( 3x^2 + 6x - 2 \)

Hint:

To differentiate a product of polynomials, first expand the expression, then apply the power rule to each term.

Answer 1

The Correct Option is B

To differentiate \( y = x(x - 1)(x - 2) \), we use the product rule. First, expand the polynomial: \[ y = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x. \] Now, differentiate term by term: \[ \frac{dy}{dx} = 3x^2 - 6x + 2. \]