Question Detail

We are given the function y = (3x - 2)(3 - x).Method 1: Expand the product first, then differentiate.y = 3x(3) + 3x(-x) - 2(3) - 2(-x) = 9x - 3x2 - 6 + 2x = -3x2 + 11x - 6.Now differentiate term by term:dy/dx = d/dx (-3x2) + d/dx (11x) - d/dx (6) = -3(2x) + 11(1) - 0 = -6x + 11 or 11 - 6x.Method 2: Use the product rule (uv)' = u'v + uv'.Let u = 3x - 2, so u' = 3.Let v = 3 - x, so v' = -1.dy/dx = (3)(3 - x) + (3x - 2)(-1) = 9 - 3x - 3x + 2 = 11 - 6x.Both methods yield the same result. This matches option D.