Question Detail
Question
Find dy/dx if 3x^2 y + xy^2 = 5
Correct Answer
Option B is the correct answer.
Detailed Explanation
This requires implicit differentiation. Differentiate both sides of the equation with respect to x, treating y as a function of x and applying the product rule where necessary.d/dx [3x2y] + d/dx [xy2] = d/dx [5](6xy + 3x2 dy/dx) + (1 * y2 + x * 2y (dy/dx)) = 06xy + 3x2 dy/dx + y2 + 2xy dy/dx = 0Group terms containing dy/dx on one side and the rest on the other:dy/dx (3x2 + 2xy) = -6xy - y2Factor out -1 from the right side:dy/dx (3x2 + 2xy) = -(y2 + 6xy)Solve for dy/dx:dy/dx = -(y2 + 6xy) / (3x2 + 2xy).
Hint
Use implicit differentiation and remember to apply the product rule for terms involving products of x and y.