The 1st term of what you quoted as the book's derivative is missing a factor of 2 from the differentiation of (14x^2 +7x-21)^2. Perhaps they corrected that error in a later step?

It should read:

.

By the way, if you intend on working that out, I'd strongly suggest getting those ugly factors of 7 factored out before you even begin:

, where c = (4)(49) = 196.

One more hint - when computing a derivative of a polynomial that you'll eventually want to factor, don't expand the polynomial. Keep it together.

What I'm saying here is do not try to expand into a 5 term 4th degree polynomial in x. Keep it factored.

One final hint: You can factor