Functions of the form \(f(x) = x^n\text{,}\) where \(n = 1, 2, 3, \ldots\text{,}\) are often called power functions. The first two questions below revisit work we did earlier in Chapter 1, and the following questions extend those ideas to higher powers of \(x\text{.}\)
Conjecture a formula for the derivative of \(f(x) = x^n\) that holds for any positive integer \(n\text{.}\) That is, given \(f(x) = x^n\) where \(n\) is a positive integer, what do you think is the formula for \(f'(x)\text{?}\)
