What is the derivative of f(x) = 3x^3 - 5x + 2?

What is the derivative of f(x) = 3x^3 - 5x + 2?

Step 1: Identify the function f(x) = 3x^3 - 5x + 2.
Step 2: Use the power rule for derivatives, which states that if f(x) = ax^n, then f'(x) = n * ax^(n-1).
Step 3: Apply the power rule to each term in the function.
Step 4: For the first term 3x^3, the derivative is 3 * 3x^(3-1) = 9x^2.
Step 5: For the second term -5x, the derivative is -5 * 1x^(1-1) = -5.
Step 6: The constant term 2 has a derivative of 0, since the derivative of any constant is 0.
Step 7: Combine the derivatives from each term: f'(x) = 9x^2 - 5 + 0.
Step 8: Simplify the expression to get f'(x) = 9x^2 - 5.

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