Answer
P'(x) = n$a_{n}x^{n-1}$ + (n-1)$a_{n-1}x^{n-2}$ + $\cdot$ $\cdot$ $\cdot$ + 3$a_{3}x^{2}$ + 2$a_{2}x$ + $a_{1}$
Work Step by Step
We take the derivative term by term. Each term is of the form $ax^{n}$, by the power rule the derivative should be $anx^{n-1}$.
The only term that is different is $a_{0}$ which is a constant, and the derivative of a constant is 0.
So each term is multiplied by its power, then one is subtracted from the power and the constant drops off and we get:
P'(x) = n$a_{n}x^{n-1}$ + (n-1)$a_{n-1}x^{n-2}$ + $\cdot$ $\cdot$ $\cdot$ + 3$a_{3}x^{2}$ + 2$a_{2}x$ + $a_{1}$
