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onegirl

  • 2 years ago

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

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

  2. onegirl
    • 2 years ago
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    no

  3. onegirl
    • 2 years ago
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    is that with the chain rule or?

  4. wio
    • 2 years ago
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    This is what is called "multiplication"

  5. onegirl
    • 2 years ago
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    ok

  6. onegirl
    • 2 years ago
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    you factor it right?

  7. onegirl
    • 2 years ago
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    let me try to expand it

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

  9. onegirl
    • 2 years ago
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    ok

  10. wio
    • 2 years ago
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    Now take the derivative.

  11. onegirl
    • 2 years ago
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    ok hold on

  12. onegirl
    • 2 years ago
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    the derivative of x^6 - 2x^3 + 1 right?

  13. wio
    • 2 years ago
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    Yeah.

  14. onegirl
    • 2 years ago
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    i got 6x^2 (x^3 - 1)

  15. wio
    • 2 years ago
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    What is the derivative of \(x^6\)?

  16. wio
    • 2 years ago
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    What is the derivative of \(-2x^3\)?

  17. onegirl
    • 2 years ago
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    its 6x^5

  18. onegirl
    • 2 years ago
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    and -6x^2 for -2x^3

  19. onegirl
    • 2 years ago
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    so it will be 6x^5 - 6x^2 ?

  20. wio
    • 2 years ago
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    Yeah. You don't need to factor it.

  21. onegirl
    • 2 years ago
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    ok

  22. onegirl
    • 2 years ago
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    so that's it?

  23. wio
    • 2 years ago
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    yes

  24. onegirl
    • 2 years ago
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    okay can did we use the chain rule on this one or? no chain rule?

  25. onegirl
    • 2 years ago
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    are u there?

  26. onegirl
    • 2 years ago
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    @wio ?

  27. sirm3d
    • 2 years ago
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    chain rule was not used

  28. onegirl
    • 2 years ago
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    okay thanks

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