I’m trying to learn some calculus. The book I chose is “Barron’s College Review Series; Mathematics; Calculus”. At the end of Chapter 5, I’m supposed to find the derivative for each formula. The formula in problem 15 is:

f(s) = s^2 * (3s^2 – 6s + 9)^4

The answer in the book is:

f ’(s) = 2s * (3s^2 – 6s + 9)^3 * (15s^2 – 18s + 9)

OK, I know that 2s is the derivative of s2, but shouldn’t the derivative of

(3s^2 – 6s + 9)^4 be

4(3s^2 – 6s + 9)^3 * (6s – 6) and shouldn’t the product rule apply so that

f ’(s) = [s^2 * 4(3s^2 – 6s + 9)^3 * (6s – 6)] + [ 2s * (3s^2 – 6s + 9)^4 ]

I believe that I am wrong because glancing ahead to problem 23, which is similar, I see that I will again have the wrong answer. I’m guessing that I either started at the wrong point or I can factor out to reduce the formula to the correct answer.

A little stumped over here. Could someone provide some guidance or insight, please?

Holy Crap! Thanks Owl.

I was stuck on this problem for a several hours. I kept trying different ways of factoring, but never could find anything that would take me in the right direction.

After reading your response, I looked at it again and (3s^2 - 6s + 9)^3 jumped right out at me. I factored it out and had the answer within a minute. Funny how you get stuck some times. I got stuck on a problem in chapter 2 that had me stumped for 2 days, then "poof" it came to me. I didn't want it to take 2 days this time.

Thanks again.