anonymous
  • anonymous
Find the derivative with and without using the chain rule. f(x) = (x^3 - 1)^2
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Do you know how to expand it? \[ (x^3-1)^2 = (x^3-1)(x^3-1) \]
anonymous
  • anonymous
no
anonymous
  • anonymous
is that with the chain rule or?

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anonymous
  • anonymous
This is what is called "multiplication"
anonymous
  • anonymous
ok
anonymous
  • anonymous
you factor it right?
anonymous
  • anonymous
let me try to expand it
anonymous
  • anonymous
Now we will use distributive property of multiplication. \[ (x^3-1)(x^3-1) = x^3(x^3-1)-1(x^3-1)=x^6-x^3-x^2+1=x^6-2x^3+1 \]
anonymous
  • anonymous
ok
anonymous
  • anonymous
Now take the derivative.
anonymous
  • anonymous
ok hold on
anonymous
  • anonymous
the derivative of x^6 - 2x^3 + 1 right?
anonymous
  • anonymous
Yeah.
anonymous
  • anonymous
i got 6x^2 (x^3 - 1)
anonymous
  • anonymous
What is the derivative of \(x^6\)?
anonymous
  • anonymous
What is the derivative of \(-2x^3\)?
anonymous
  • anonymous
its 6x^5
anonymous
  • anonymous
and -6x^2 for -2x^3
anonymous
  • anonymous
so it will be 6x^5 - 6x^2 ?
anonymous
  • anonymous
Yeah. You don't need to factor it.
anonymous
  • anonymous
ok
anonymous
  • anonymous
so that's it?
anonymous
  • anonymous
yes
anonymous
  • anonymous
okay can did we use the chain rule on this one or? no chain rule?
anonymous
  • anonymous
are u there?
anonymous
  • anonymous
@wio ?
sirm3d
  • sirm3d
chain rule was not used
anonymous
  • anonymous
okay thanks

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