Question: Differentiate the following expression with respect to $x$: $$f(x) = 3x^6 - x^4 + 2x - 9$$
1. **State the problem:** Differentiate the function $$f(x) = 3x^6 - x^4 + 2x - 9$$ with respect to $$x$$.
2. **Recall the differentiation rule:** The derivative of $$x^n$$ with respect to $$x$$ is $$nx^{n-1}$$.
3. **Apply the power rule to each term:**
- Derivative of $$3x^6$$ is $$3 \times 6 x^{6-1} = 18x^5$$.
- Derivative of $$-x^4$$ is $$-1 \times 4 x^{4-1} = -4x^3$$.
- Derivative of $$2x$$ is $$2 \times 1 x^{1-1} = 2$$.
- Derivative of constant $$-9$$ is $$0$$.
4. **Combine all derivatives:**
$$f'(x) = 18x^5 - 4x^3 + 2$$
**Final answer:** $$\boxed{f'(x) = 18x^5 - 4x^3 + 2}$$