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FreeTrader

  • 4 years ago

Can you help me understand how to differentiate involving logarithms? Please see the Q for an example...

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  1. FreeTrader
    • 4 years ago
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    \[f(x) = x^2\log_{2} (x^2+1)\]

  2. amistre64
    • 4 years ago
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    the log2 is best viewed as ln(x^2+1)/ln(2)

  3. amistre64
    • 4 years ago
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    since 1/ln(2) is a constant, all thats left is to consider this as a usual ln(u) type issue

  4. FreeTrader
    • 4 years ago
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    I understand to start by converting the log base 2 into a natural ln base e, which leads to: \[f(x)=x^2(\ln (x^2 + 1) /\ln 2)\] I am unsure how to address the fractional term involving the ln's.

  5. amistre64
    • 4 years ago
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    1/ln(2) is a constant; nothing changes about it ... so

  6. amistre64
    • 4 years ago
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    remove it, stick it to the side, put a stick note on top ot it and work the rest of the problem

  7. FreeTrader
    • 4 years ago
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    Ah, the 1/ln2 is a constant. Good insight. Thank you, @amistre64.

  8. FreeTrader
    • 4 years ago
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    what is a stick note?

  9. amistre64
    • 4 years ago
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    sticky note is what thats spose to be, a post it note, something to remind you not to forget about it in the end :)

  10. FreeTrader
    • 4 years ago
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    okay, got it.

  11. FreeTrader
    • 4 years ago
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    I think the key to this one for me was recognizing that constant.

  12. amistre64
    • 4 years ago
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    yep

  13. FreeTrader
    • 4 years ago
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    Would I then use the product rule against the remaining terms x^2 and ln(x^2+1) ?

  14. amistre64
    • 4 years ago
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    i would, seeing how its a product ;)

  15. FreeTrader
    • 4 years ago
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    Sometimes all the new stuff to learn can create uncertainty of the obvious.

  16. amistre64
    • 4 years ago
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    yeah, im dong that with existence and uniquenes thrms right now wondering what gppd to do and stuff

  17. amistre64
    • 4 years ago
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    good to do and stuff ... cant type

  18. FreeTrader
    • 4 years ago
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    What class are you taking at this time?

  19. amistre64
    • 4 years ago
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    im in college going to take linear algebra, calc3, and diffy qs in the spring

  20. FreeTrader
    • 4 years ago
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    I am taking Calc 1.

  21. FreeTrader
    • 4 years ago
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    And reviewing precalc daily!

  22. FreeTrader
    • 4 years ago
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    Thanks, best wishes.

  23. amistre64
    • 4 years ago
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    good luck :)

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