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

To find the derivative of the function f(x) = x², we use the power rule of differentiation, which states that if you have a function in the form of f(x) = x^n, where n is any real number, the derivative f'(x) can be computed using the formula f'(x) = n * x^(n-1).

In this case, n is 2 since the function is x². Applying the power rule:

1. Multiply the exponent (2) by the coefficient (which is 1, as there is no specified coefficient) to get 2.

2. Decrease the exponent by 1, changing it from 2 to 1.

This results in the derivative being 2 * x^(2-1), which simplifies to 2x.

Thus, the derivative of the function f(x) = x² is indeed 2x. This outcome reflects how the slope of the tangent line to the curve of the function changes as x changes. The function grows linearly faster as x increases, signifying that for every increase in x, the output of the function increases at a rate determined by 2x.