Question

Find the coefficient of the squared term in the simplified form for the second derivative., f"(x) for f(x)=(X^3+2x+3)(3x^3-6x^2-8x+1). use the hyphen symbol,-, for negative values.

Answer 1

Hey Maggy :)\[\large\rm f(x)=(x^3+2x+3)(3x^3-6x^2-8x+1)\]Hmm this one looks like a doozy.
Remember your product rule?

Answer 2

\[\rm \color{royalblue}{f'(x)}=\color{royalblue}{(x^3+2x+3)'}(3x^3-6x^2-8x+1)+(x^3+2x+3)\color{royalblue}{(3x^3-6x^2-8x+1)'}\]This is how we would "set up" our first derivative, ya? :d

Answer 3

Alternatively, you could expand out all the brackets from the start.
That might actually be easier :)
Hmm I'm not sure.

Answer 4

ya ya ya ya, expand first.
that seems way better >.<
Otherwise we have to combine a whole lot of term at the end..
my bad

Answer 5

we allowed to do that, ya? :d

Answer 6

my head hurts trying to follow you lol so we expand?

Answer 7

ya let's try that instead :)
product rule will result in two groups of stuff.
second derivative will require product rule twice more.
then expanding three sets of things, and combining.

expanding first seems way simpler