Let $f(x) = x^{2n} - x^{2n-1} + \cdots + x^4 - x^3 + x^2 - ax + b$
We wish to compute f'(1). The way I did this was to differentiate term by term, and then pair the terms of the form $-(2m + 1)x^{2m} + (2m) x^{2m-1}$ to get $-1$ summed $n-1$ times to get a $1-n$ term. Considering the first and last terms, we see that $2n$ and $-a$ contribute a term. So we get f'(1) = n+1-a
My book just states that f'(1) = n-1+2-a. They might have a quicker way than my reasoning, and I am not sure where the $+2$ comes from. Does anyone see how the book did it?