Final answer:
The question involves calculus, specifically the differentiation of a function f(x)=x^n using the power rule. The power rule states that the derivative is nx^(n-1), where 'n' is the original exponent.
Step-by-step explanation:
The subject of this question is the differentiation of a function with a variable raised to a power, specifically f(x)=x^n. This topic falls under the category of calculus, which is often studied in high school or college mathematics. To differentiate f(x)=x^n, we apply the power rule, which states that the derivative of x^n is nx^(n-1). Simply put, we bring down the exponent as a coefficient in front of x and subtract one from the original exponent.
For example, if our function was f(x)=x^4, the derivative would be 4x^(4-1) or 4x^3. It is also essential to remember that exponents indicate how many times a number is multiplied by itself and that negative exponents give us the reciprocal of the base raised to the positive exponent. Furthermore, differentiation can be applied term by term when dealing with polynomial functions.