Given the polynomial function p(x) = 2x^3 + x^2 - 2x - 5, find the derivative, p^'(x), using the definition of a derivative. Which of the following options correctly represents p^'(x)?
Options:
A) 6x^2 + 2x - 2
B) 6x^2 + 2x + 2
C) 6x^2 - 2x - 2
D) 6x^2 - 2x + 2