What is the derivative of x raised to the power n?

The derivative of a function describes the rate at which the function's value changes as the input changes. When dealing with a power function like (x^n), where (n) is a constant, the power rule is applied to find its derivative.

According to the power rule, when you differentiate (x^n), you multiply the term by the exponent (n) and then subtract 1 from that exponent. This gives the derivative as (nx^{(n-1)}).

So, for (x^n):

1. Multiply (x^n) by the exponent (n).

2. Reduce the exponent by 1, resulting in (x^{n-1}).

Thus, the correct result of differentiating (x^n) is (nx^{(n-1)}), which is why that choice is correct. This rule is fundamental in calculus and applies to all real numbers (n) where (x) is in the domain of the function.