Implicit differentiation - Help please!

Probably simple, but it's not exactly apparent to me...

1. y^3 - x^2 -1 =x^2 - 3x

A. Find dy/dx. **I came up with y'= 4x-3 / 3y^2 for this part.

B. Use algebra to solve for y. **I said y= (2x^2 - 3x + 1)^(1/3)

C. Use "traditional methods" to differentiate y from part B.

**WHAT? Do I use the quadratic formula here?

And then cube the answers?

D. Show that the answers in part A and C are the same using algebra.

**Maybe after I figure out what to do with part C,

this will become clear.

And now for what I think is probably an easy one:

2. A particle is moving along the graph of the function y= x^2 + 3x - 5 at a rate of dx/dt = 3cm/s. Find the rate of change of the particle in the y direction dy/dt, when x=1.

**Do I take the natural log of each side first? Then, solve for y', plug in x=1? What do I do with the 3cm/s?

Hopefully someone can give me a jump start. :) Thanks.