Functions of the form f(x) = x^n , where n = 1, 2, 3, \ldots , are often
called * power functions. *

(a) Use the limit definition of the derivative to find

(b) Use the limit definition of the derivative to find

(c) Use the limit definition of the derivative to find

(d) Based on your work in (a), (b), and (c), what do you conjecture is the derivative of

Of

(e) Conjecture a formula for the derivative of

You can earn partial credit on this problem.