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amyna

  • one year ago

find the derivative: f(x)=(ln x^2)^3 The answer is: 24(lnx)^2/x i have no idea where to start! plz help!!

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  1. amyna
    • one year ago
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    |dw:1442084297389:dw|

  2. Jhannybean
    • one year ago
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    Do you know how the chain rule works?

  3. hartnn
    • one year ago
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    a possible first step would be to use \(\ln a^b = b \ln a\)

  4. hartnn
    • one year ago
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    actually, the chain rule is \(\sf \frac{d}{dx} (f(g(h(x))))= f'(g(h(x))) \cdot g'(h(x)) \cdot h'(x)\)

  5. amyna
    • one year ago
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    ok so when i used the chain rule, so far i have: 3(lnx^2)^2 (1/x * 2x)

  6. amyna
    • one year ago
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    is that the correct way to start?

  7. hartnn
    • one year ago
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    whats the derivative of ln x^2 ?

  8. amyna
    • one year ago
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    right its 1/x^2 *2x

  9. hartnn
    • one year ago
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    think chain rule example: if I wanted derivative if sin^2 x it would be 2 sin x* (derivative of sin x) because derivative of x^2 is 2x

  10. hartnn
    • one year ago
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    so try once more, whats the derivative of ln x^2 ?

  11. hartnn
    • one year ago
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    a much better start would be to use \(\Large \ln x^2 = 2\ln x \)

  12. amyna
    • one year ago
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    2/x ?

  13. hartnn
    • one year ago
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    thats the derivative of 2 ln x starting again, f(x) = (2 ln x)^3 = 2^3 (ln x)^3 makes sense??

  14. amyna
    • one year ago
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    2lnx/x

  15. hartnn
    • one year ago
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    2^3 = 8 applying chain rule for (ln x)^3 is easier. try it

  16. amyna
    • one year ago
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    3(lnx)^2 *( 1/x)

  17. hartnn
    • one year ago
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    perfect! now multiply that with 8

  18. amyna
    • one year ago
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    oh okay! got it Thanks so much!! :)

  19. hartnn
    • one year ago
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    welcome ^_^

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