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onegirl Group Title

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

  • one year ago
  • one year ago

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

    • one year ago
  2. onegirl Group Title
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    no

    • one year ago
  3. onegirl Group Title
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    is that with the chain rule or?

    • one year ago
  4. wio Group Title
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    This is what is called "multiplication"

    • one year ago
  5. onegirl Group Title
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    ok

    • one year ago
  6. onegirl Group Title
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    you factor it right?

    • one year ago
  7. onegirl Group Title
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    let me try to expand it

    • one year ago
  8. wio Group Title
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    Now we will use distributive property of multiplication. \[ (x^3-1)(x^3-1) = x^3(x^3-1)-1(x^3-1)=x^6-x^3-x^2+1=x^6-2x^3+1 \]

    • one year ago
  9. onegirl Group Title
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    ok

    • one year ago
  10. wio Group Title
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    Now take the derivative.

    • one year ago
  11. onegirl Group Title
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    ok hold on

    • one year ago
  12. onegirl Group Title
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    the derivative of x^6 - 2x^3 + 1 right?

    • one year ago
  13. wio Group Title
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    Yeah.

    • one year ago
  14. onegirl Group Title
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    i got 6x^2 (x^3 - 1)

    • one year ago
  15. wio Group Title
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    What is the derivative of \(x^6\)?

    • one year ago
  16. wio Group Title
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    What is the derivative of \(-2x^3\)?

    • one year ago
  17. onegirl Group Title
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    its 6x^5

    • one year ago
  18. onegirl Group Title
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    and -6x^2 for -2x^3

    • one year ago
  19. onegirl Group Title
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    so it will be 6x^5 - 6x^2 ?

    • one year ago
  20. wio Group Title
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    Yeah. You don't need to factor it.

    • one year ago
  21. onegirl Group Title
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    ok

    • one year ago
  22. onegirl Group Title
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    so that's it?

    • one year ago
  23. wio Group Title
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    yes

    • one year ago
  24. onegirl Group Title
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    okay can did we use the chain rule on this one or? no chain rule?

    • one year ago
  25. onegirl Group Title
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    are u there?

    • one year ago
  26. onegirl Group Title
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    @wio ?

    • one year ago
  27. sirm3d Group Title
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    chain rule was not used

    • one year ago
  28. onegirl Group Title
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    okay thanks

    • one year ago
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