Question

Differentiate the function and express answer in simplified factored form.

Answer 1

\[y=(x^2+3)^3(x^3+3)^2\]

Answer 2

product + chain rule

Answer 3

i've tried and i can't get the right answer

Answer 4

show your attempt.

Answer 5

am I supposed to derive (x^2+3)^3 and (x^3+3)^2 separately, then use product rule to get the final answer?

Answer 6

\[\Large\bf\sf y=(x^2+3)^3(x^3+3)^2\]Setup your product rule first,\[\Large\bf\sf y'=\color{royalblue}{\left[(x^2+3)^3\right]'}(x^3+3)^2+(x^2+3)^3\color{royalblue}{\left[(x^3+3)^2\right]'}\]

Answer 7

Take derivative of the blue parts.
Power rule, then chain rule.

Answer 8

or you can make your life miserable by expanding first then just apply the power rule

Answer 9

heh, true :3

Answer 10

\[y'= 3(x^2+3)^2(2x)(x^3+3)^2+2(x^3+3)(3x^2)(x^2+3)^3\]
?

Answer 11

Mmmmmmm ya looks good!

Answer 12

Simplify that beast down a bit!

Answer 13

Am I supposed to factor things out or no?

Answer 14

factor if u can

Answer 15

The first term has two (x^2+3)'s,
the second term has only one.

So factor out the greatest factor,
which is just one of them.

Factor (x^2+3) out of each term.
Do the same for your (x^3+3)'s.

And also with the loose x's in front.

Answer 16

Oh the second term had three (x^2+3)'s, my bad :P hehe

Answer 17

\[y'=(x^3+3)+x(x^2+3)\]

Answer 18

hmmmmm

*pokes zepdrix* rofl

Answer 19

o-o"