College Math Placement Practice Test 2026 – Comprehensive All-in-One Guide for Exam Success!

Question: 1 / 400

What is the derivative of f(x) = x^3?

2x^2

3x^2

The derivative of a function gives the rate at which the function's output changes with respect to its input. For the function \( f(x) = x^3 \), we can apply the power rule of differentiation. The power rule states that if \( f(x) = x^n \), then the derivative \( f'(x) \) is calculated as \( f'(x) = n \cdot x^{n-1} \).

In this case, applying the power rule to \( f(x) = x^3 \):

1. Identify \( n \): Here, \( n = 3 \).

2. Apply the power rule: \( f'(x) = 3 \cdot x^{3-1} = 3 \cdot x^2 \).

Thus, the derivative of \( f(x) = x^3 \) is \( 3x^2 \). This is why the correct answer is \( 3x^2 \). The other options do not align with the application of the power rule for this specific exponent.

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x^2

2x

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