Using implicit differentiation, find dy/dx. √xy=-4+yx^3

Answer 1

√xy = - 4 + yx³; 1/2(xy)^-1/2(y + xdy/dx) = 0 + 3yx² + x³dy/dx; 1/2(xy)^-1/2y - 3yx² = (x³ - 1/2(xy)^-1/2·x)dy/dx;

dy/dx = (x^-1/2y^1/2 - 6yx²)/(2x³ - x^1/2y^-1/2)