What is the derivative of f(x) = 5x^3 - 2x + 1? (2023)

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Question: What is the derivative of f(x) = 5x^3 - 2x + 1? (2023)

Options:

Correct Answer: 15x^2 - 2

Exam Year: 2023

Solution:

The derivative f\'(x) = 15x^2 - 2.

What is the derivative of f(x) = 5x^3 - 2x + 1? (2023)

What is the derivative of f(x) = 5x^3 - 2x + 1? (2023)

Step 1: Identify the function f(x) = 5x^3 - 2x + 1.
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 the first term 5x^3: The derivative is 3 * 5x^(3-1) = 15x^2.
Step 4: Apply the power rule to the second term -2x: The derivative is 1 * -2x^(1-1) = -2.
Step 5: The last term is a constant (1), and the derivative of a constant is 0.
Step 6: Combine the derivatives from Steps 3, 4, and 5: f'(x) = 15x^2 - 2 + 0.
Step 7: Simplify the expression: f'(x) = 15x^2 - 2.

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