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



This Question is Closed

wio
Best Response
You've already chosen the best response.
0
Do you know how to expand it? \[
(x^31)^2 = (x^31)(x^31)
\]

onegirl
Best Response
You've already chosen the best response.
0
no

onegirl
Best Response
You've already chosen the best response.
0
is that with the chain rule or?

wio
Best Response
You've already chosen the best response.
0
This is what is called "multiplication"

onegirl
Best Response
You've already chosen the best response.
0
ok

onegirl
Best Response
You've already chosen the best response.
0
you factor it right?

onegirl
Best Response
You've already chosen the best response.
0
let me try to expand it

wio
Best Response
You've already chosen the best response.
0
Now we will use distributive property of multiplication. \[
(x^31)(x^31) = x^3(x^31)1(x^31)=x^6x^3x^2+1=x^62x^3+1
\]

onegirl
Best Response
You've already chosen the best response.
0
ok

wio
Best Response
You've already chosen the best response.
0
Now take the derivative.

onegirl
Best Response
You've already chosen the best response.
0
ok hold on

onegirl
Best Response
You've already chosen the best response.
0
the derivative of x^6  2x^3 + 1 right?

wio
Best Response
You've already chosen the best response.
0
Yeah.

onegirl
Best Response
You've already chosen the best response.
0
i got 6x^2 (x^3  1)

wio
Best Response
You've already chosen the best response.
0
What is the derivative of \(x^6\)?

wio
Best Response
You've already chosen the best response.
0
What is the derivative of \(2x^3\)?

onegirl
Best Response
You've already chosen the best response.
0
its 6x^5

onegirl
Best Response
You've already chosen the best response.
0
and 6x^2 for 2x^3

onegirl
Best Response
You've already chosen the best response.
0
so it will be 6x^5  6x^2 ?

wio
Best Response
You've already chosen the best response.
0
Yeah. You don't need to factor it.

onegirl
Best Response
You've already chosen the best response.
0
ok

onegirl
Best Response
You've already chosen the best response.
0
so that's it?

wio
Best Response
You've already chosen the best response.
0
yes

onegirl
Best Response
You've already chosen the best response.
0
okay can did we use the chain rule on this one or? no chain rule?

onegirl
Best Response
You've already chosen the best response.
0
are u there?

onegirl
Best Response
You've already chosen the best response.
0
@wio ?

sirm3d
Best Response
You've already chosen the best response.
1
chain rule was not used

onegirl
Best Response
You've already chosen the best response.
0
okay thanks