Answer
See below.
Work Step by Step
Let us take the following polynomial:
$p(x)=a_{n}x^n+a_{n-1}x^{(n-1)}+............+a_{0}$
We wish to take the derivative of the above:
$p'(x)=(a_{n}x^n+a_{n-1}x^{(n-1)}+............+a_{0})'$
According to rule C, we get:
$p'(x)=(a_{n}x^n)'+(a_{n-1}x^{(n-1)})'+............+(a_{0})'$
According to rule B, we get:
$p'(x)=a_{n}(x^n)'+a_{n-1}(x^{(n-1)})'+............+a_{1}(x)'$
According to rule A, we get:
$p'(x)=na_{n}x^{(n-1)}+(n-1)(a_{n-1}x^{(n-2)})+............+(a_{1})$
Which gives us the final derivative function.
