The given function is:

$g(s) = \frac{2s^2 - 9s + 6}{s^2}$

We need to find $g'(s)$, the derivative of $g(s)$.

Step 1: Rewrite the function

First, simplify $g(s)$ by splitting the terms:

$g(s) = \frac{2s^2}{s^2} - \frac{9s}{s^2} + \frac{6}{s^2}$ $g(s) = 2 - \frac{9}{s} + \frac{6}{s^2}$

Step 2: Differentiate each term

Now, apply the power rule to differentiate each term.

1. $\frac{d}{ds}(2) = 0$
2. $\frac{d}{ds}\left(-\frac{9}{s}\right) = \frac{9}{s^2}$ (since $\frac{d}{ds}\left(\frac{1}{s}\right) = -\frac{1}{s^2}$)
3. $\frac{d}{ds}\left(\frac{6}{s^2}\right) = -\frac{12}{s^3}$ (using the power rule for $s^{-2}$)

Step 3: Combine the derivatives

Thus, the derivative is:

$g'(s) = 0 + \frac{9}{s^2} - \frac{12}{s^3}$ $g'(s) = \frac{9}{s^2} - \frac{12}{s^3}$

Step 4: Check the answer choices

The correct answer is:

$\boxed{\frac{9}{s^2} - \frac{12}{s^3}}$

This matches the last option in the given multiple-choice list.

Do you need further details on any steps or have additional questions? Here are some related questions for practice:

1. How do you apply the power rule for negative exponents?
2. What happens when differentiating a constant term?
3. How does the quotient rule compare to simplifying first, as done here?
4. What is the derivative of $\frac{1}{s^n}$ in general?
5. How do you find the second derivative of $g(s)$?

Tip: Always try to simplify expressions before differentiating to avoid complicated rules like the quotient rule.