Start with an equation : y^{3} = xy + 1 
Differentiate both sides
Note 1 : Chain rule needed for y^{3}
Note 2 : Product rule needed for xy 
d
dx 
y^{3} = 
d
dx 
(xy + 1) 

3y^{2}y' =
(1y + xy' ) + 0 
Move all y' terms to the left side 
3y^{2}y'  xy' = y 
Factor out y' in the left side 
y'(3y^{2}  x) = y 
Divide by the factor without y' 
y' = 
y
3y^{2}  x 
