Step 1: Define the function.
The function provided is:
\[
f(x) = 3x^3 - 5x^2 + 2x - 4
\]
Step 2: Apply the power rule for differentiation.
The power rule dictates that the derivative of \( ax^n \) is \( a \cdot n \cdot x^{n-1} \).
Differentiating each term individually yields:
\[
\frac{d}{dx}(3x^3) = 9x^2
\]
\[
\frac{d}{dx}(-5x^2) = -10x
\]
\[
\frac{d}{dx}(2x) = 2
\]
\[
\frac{d}{dx}(-4) = 0
\]
Step 3: Sum the derivatives.
The derivative of \( f(x) \) is obtained by summing the individual derivatives:
\[
f'(x) = 9x^2 - 10x + 2
\]
Answer: The derivative is \( 9x^2 - 10x + 2 \).