Question Detail
Question
Find dy/dx if 3x2y + xy2 = 5.
Correct Answer
Option B is the correct answer.
Detailed Explanation
Differentiate both sides of the equation implicitly with respect to x.d/dx(3x2y) + d/dx(xy2) = d/dx(5)Apply the product rule for the terms on the left:(6xy + 3x2 dy/dx) + (y2 + x * 2y dy/dx) = 0Group terms with dy/dx:3x2 dy/dx + 2xy dy/dx = -6xy - y2Factor out dy/dx:dy/dx (3x2 + 2xy) = -(6xy + y2)Solve for dy/dx:dy/dx = -(y2 + 6xy) / (3x2 + 2xy).This matches option B.
Hint
Use implicit differentiation. Remember to apply the product rule and treat y as a function of x (so dy/dx appears when differentiating y terms).