An alternative way to do implicit differentiation is to introduce a mythical extra variable t. Think of x and y as both functions of t. Now, use the fact that
(a) Solve for dy/dx.
(b) For the equation x2 + y3 = 6 Find the relationship between the rates of change of x and y as in the previous section.
(c) Use the result of parts (a) and (b) to find y'