MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
For a positive integer n, define pn(x)=xn for all real x.
(a) Derive a general expression for pn′(x) in terms of n and x. Your derivation must be valid for all integers n≥1. Clearly state each algebraic step.
(b) Using your result from part (a), find p6′(2).
(c) Describe how your formula in part (a) would need to be adapted, if at all, for negative integer exponents.