1. **Differentiate the expression** $9x^2 - \frac{3}{x^2}$ with respect to $x$. 2. Use the power rule for differentiation: if $f(x) = x^n$, then $f'(x) = nx^{n-1}$. 3. Rewrite the expression to apply the power rule easily: $$9x^2 - 3x^{-2}$$ 4. Differentiate term-by-term: $$\frac{d}{dx}(9x^2) = 9 \times 2x^{2-1} = 18x$$ $$\frac{d}{dx}(-3x^{-2}) = -3 \times (-2)x^{-2-1} = 6x^{-3}$$ 5. Combine the derivatives: $$18x + 6x^{-3}$$ 6. Final answer: $$\boxed{18x + \frac{6}{x^3}}$$ This completes the differentiation of the first expression. Note: The user asked multiple questions but per instructions, only the first problem is solved completely.