The first screen is the problem. The second is my work. I worked this problem out twice and got the same answer twice. Since Latex is still down this out to make it a bit easier to read.
Thanks for your help!
ok, the answer you have in the second slot seems to be the closest to the answer (well, it is the answer, it just looks messier than it has to be). after that, you seem to have restarted the problem. anyway, here are some things to fix up, nothing major, you handled it well, just to make things look a bit more presentable.
in the second slot:
turn 3(3x + 1)^2 * 3 into 9(3x + 1)^2
turn (3x + 1)^3 * [e^(x^2) * 2x] into 2x(3x + 1)^3 * e^(x^2)
turn (1/2)(2x^4 + 1)^(-1/2) * 8x^3 into (4x^3)(2x^4 + 1)^(-1/2)
also you have [(2x^4 + 1)^(1/2)]^2 in the denominator. the square cancels with the 1/2 power so just write (2x^4 + 1)
in the last slot: (we're not using this one, just wanted to show you something)
you left out the 2x. you have e^(x^2) * 2 in the first term, it should be e^(x^2) * 2x or 2x*e^(x^2)
now this problem can be simplified more, but i wouldn't ask you to do that, it's just a big mess. so just make thos simple corrections to the second slot, and use that as your answer. if you're feeling brave, you can factorize and simplify some stuff, i don't recommend it however
Also if a test clearly stated at the top: DO NOT SIMPLIFY; when does fundamental math principles turn into (over) simplification? I mean from his lectures he seems content on us just putting the problem in the correct form using d/dx. To him this is the correct answer because it isn't simplified at all. Also I am beginning to see the advantage of using d/dx to show someone how you got the answer, however at times it just seems a bit redundant. It takes a simple quarter of a page problem and turns it into a full page.
i agree, personally i dont write d/dx and all that stuff when i'm doing problems like these. anyway, if that's what your professor wants, give it to him. taking it one step after the d/dx is good enough of an answer, so what you wrote should be ok. if i was doing the problem, my next step would have the corrections that i gave you, i kind of simplify it a bit in my head before writing the next line. "ok, we have a (1/2) here and an 8x^3 at the back, so i'll write down 4x^3 at the front and multiply everything else"