We use the Quotient Rule: d/dx [u/v] = (vdu/dx - udv/dx) / v². Here, u = x and v = sin(x). Therefore, du/dx = 1 and dv/dx = cos(x). Substituting these into the formula: dy/dx = (sin(x) * 1 - x * cos(x)) / (sin(x))² = (sin(x) - x*cos(x)) / sin²(x). Option B reverses the order of the numerator terms (leading to a sign error), Option C incorrectly uses addition instead of subtraction, and Option D is a common mistake where students differentiate numerator and denominator independently (violating the quotient rule).