Question

Find the derivative with and without using the chain rule. f(x) = (x^3 - 1)^2

Answer 1

Do you know how to expand it? \[
(x^3-1)^2 = (x^3-1)(x^3-1)
\]

Answer 2

no

Answer 3

is that with the chain rule or?

Answer 4

This is what is called "multiplication"

Answer 5

ok

Answer 6

you factor it right?

Answer 7

let me try to expand it

Answer 8

Now we will use distributive property of multiplication. \[
(x^3-1)(x^3-1) = x^3(x^3-1)-1(x^3-1)=x^6-x^3-x^2+1=x^6-2x^3+1
\]

Answer 9

ok

Answer 10

Now take the derivative.

Answer 11

ok hold on

Answer 12

the derivative of x^6 - 2x^3 + 1 right?

Answer 13

Yeah.

Answer 14

i got 6x^2 (x^3 - 1)

Answer 15

What is the derivative of \(x^6\)?

Answer 16

What is the derivative of \(-2x^3\)?

Answer 17

its 6x^5

Answer 18

and -6x^2 for -2x^3

Answer 19

so it will be 6x^5 - 6x^2 ?

Answer 20

Yeah. You don't need to factor it.

Answer 21

ok

Answer 22

so that's it?

Answer 23

yes

Answer 24

okay can did we use the chain rule on this one or? no chain rule?

Answer 25

are u there?

Answer 26

@wio ?

Answer 27

chain rule was not used

Answer 28

okay thanks