What is the derivative of f(x) = x²?

To find the derivative of the function f(x) = x², we apply the power rule of differentiation. The power rule states that if you have a function in the form of f(x) = x^n, where n is a constant, the derivative f'(x) is given by multiplying the exponent by the base raised to the power of (n-1).

In this case, f(x) = x² means n = 2. Therefore, applying the power rule:

1. First, bring down the exponent (2) as a coefficient.

2. Next, reduce the exponent by 1, which means we subtract 1 from 2, resulting in 1.

Combining these steps, the derivative f'(x) = 2 * x^(2 - 1) simplifies to f'(x) = 2x.

This shows why the derivative of the function x² is 2x, confirming that the correct answer is indeed 2x. It's a fundamental principle in calculus that helps in understanding how functions change with respect to changes in their input.