1. Problem: Find the derivative of the function $f(x) = \frac{2}{3} x^{-3}$.\n\n2. Recall the power rule for derivatives: If $f(x) = ax^n$, then $f'(x) = a n x^{n-1}$.\n\n3. Apply the power rule to $f(x)$:\n$$f'(x) = \frac{2}{3} \times (-3) x^{-3 - 1} = \frac{2}{3} \times (-3) x^{-4}$$\n\n4. Simplify the coefficient:\n$$f'(x) = -2 x^{-4}$$\n\n5. Rewrite the derivative in a more standard form:\n$$f'(x) = -\frac{2}{x^4}$$\n\n6. Final answer: The derivative of $f(x) = \frac{2}{3} x^{-3}$ is\n$$f'(x) = -\frac{2}{x^4}$$\nThis derivative represents the rate of change of the function at any point $x \neq 0$.