Question

How would you differentiate?
f(x) = (3x^4 + 8)^2
what rule?

Answer 1

Hmm looks like chain rule.
We start with power rule on the outer function (leaving the inside the same).

Answer 2

2(3x^4+8)

Answer 3

Good, now chain rule tells us to make a copy of the inner function, take it's derivative and multiply.

Answer 4

\[\Large f'(x)\quad=\quad 2(3x^4+8)\color{royalblue}{(3x^4+8)'}\]

Answer 5

But then on the inside..? (3x^4+8) 12x^3

Answer 6

Hmm? :o

Answer 7

So my answer is 2(3x^4+8)*12x^3? Then multiply 2 and 12x^3 and get 12x^3(3x^4+8)?

Answer 8

24x^3*

yah :) you've got the right idea !

Answer 9

Sorry I mean 24 for the final answer

Answer 10

Then for my test I have to distribute it :(