Question Detail

We need to use implicit differentiation with respect to x.Differentiate each term with respect to x, remembering that y is a function of x:d/dx(3x2y) + d/dx(xy2) = d/dx(5)Using the product rule for the first two terms:(d/dx(3x2) · y + 3x2 · dy/dx) + (d/dx(x) · y2 + x · d/dx(y2)) = 0(6xy + 3x2 dy/dx) + (1 · y2 + x · 2y dy/dx) = 06xy + 3x2 dy/dx + y2 + 2xy dy/dx = 0Group terms containing dy/dx:(3x2 + 2xy) dy/dx = -6xy - y2Factor out dy/dx and solve:dy/dx = -(y2 + 6xy) / (3x2 + 2xy).