1. The problem is to find the derivative of the function $f(x) = 3x^3 - 2$ using calculus. 2. The formula for the derivative of a power function $x^n$ is given by the power rule: $$\frac{d}{dx} x^n = n x^{n-1}$$ 3. Apply the power rule to each term of $f(x)$: - For $3x^3$, the derivative is $3 \times 3x^{3-1} = 9x^2$. - For the constant $-2$, the derivative is $0$ because the derivative of any constant is zero. 4. Combine the results: $$f'(x) = 9x^2 + 0 = 9x^2$$ 5. Therefore, the derivative of the function $f(x) = 3x^3 - 2$ is: $$f'(x) = 9x^2$$ This derivative tells us the rate of change of the function at any point $x$.