3y^2 +xy = x^3 + 10
Treat y as a function of x and take the derivative of each side with respect to x
3 * 2y ( dy/dx) + x * dy /dx + y *1 = 3x^2 + 0
6y dy /dx + x dy/dx +y = 3x^2
Subtract y
6y dy/dx + x dy/dx = 3x^2 -y
Factor out the dy/dx
dy/dx ( 6y +x) = 3x^2 -y
Divide by (6y+x)
dy/dx = ( 3x^2 -y)/ (6y+x)
