Conquer the College Math Placement Challenge 2026 – Step Up and Shine!

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Question: 1 / 400

What is the derivative of the function f(x) = 3x²?

To find the derivative of the function $ f(x) = 3x^2 $, we apply the power rule, which states that if you have a term in the form $ ax^n $, the derivative is given by multiplying the coefficient $ a $ by the exponent $ n $ and then reducing the exponent by one.

In this function, we identify $ a = 3 $ and $ n = 2 $. According to the power rule, the derivative $ f'(x) $ can be computed as follows:

1. Multiply the coefficient (3) by the exponent (2), which gives us $ 3 \cdot 2 = 6 $.

2. Reduce the exponent by one, changing the exponent from 2 to 1.

Thus, the derivative $ f'(x) = 6x^1 $, which simplifies to $ f'(x) = 6x $. This is why the correct answer is the derivative $ 6x $.

This approach and understanding of the power rule are fundamental in calculus, making it essential to master as it allows us to find the slope of any polynomial function accurately.

Conquer the College Math Placement Challenge 2026 – Step Up and Shine!

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