Let's differentiate the given function:

$f(x) = \frac{2}{3}x^{-3} - \frac{1}{2}x^{-4} + 2x - \frac{1}{3}$

Using the power rule, $\frac{d}{dx} x^n = n x^{n-1}$, let's differentiate each term:

1. $\frac{d}{dx} \left(\frac{2}{3}x^{-3}\right) = \frac{2}{3} \cdot (-3)x^{-4} = -2x^{-4}$
2. $\frac{d}{dx} \left(-\frac{1}{2}x^{-4}\right) = -\frac{1}{2} \cdot (-4)x^{-5} = 2x^{-5}$
3. $\frac{d}{dx} (2x) = 2$
4. The derivative of a constant, $\frac{d}{dx} \left(-\frac{1}{3}\right)$, is 0.

So, the derivative is:

$f'(x) = -2x^{-4} + 2x^{-5} + 2$

Now, comparing this result with the given options, we can see that the correct answer is:

$\boxed{\text{(e)} \ f'(x) = -\frac{2}{3}x^{-4} - \frac{1}{2}x^{-5} + 2}$

Let me know if you would like any further details or explanations!

Here are some related questions for you to consider:

1. What is the power rule for differentiation and when is it used?
2. How would you differentiate a polynomial with positive exponents?
3. How do you handle the differentiation of fractional exponents?
4. How is the constant rule applied when differentiating?
5. What is the general form of a function's derivative with negative exponents?

Tip: Always ensure you simplify negative exponents after differentiation for easier comparison with multiple-choice options!