Question Detail

We use implicit differentiation. Differentiate each term with respect to x:d/dx (3x²y) + d/dx (xy²) = d/dx (5)Apply the product rule for the first two terms:(6xy + 3x² dy/dx) + (y² + x(2y dy/dx)) = 06xy + 3x² dy/dx + y² + 2xy dy/dx = 0Group terms containing dy/dx on one side and the remaining terms on the other:(3x² + 2xy) dy/dx = -6xy - y²Factor out dy/dx and solve:dy/dx = -(6xy + y²) / (3x² + 2xy).This matches option B.