# Chapter 3 - Questions to Guide Your Review - Page 201: 9

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.

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