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Can you help me understand how to differentiate involving logarithms? Please see the Q for an example...
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\[f(x) = x^2\log_{2} (x^2+1)\]
amistre64
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the log2 is best viewed as ln(x^2+1)/ln(2)
amistre64
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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
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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.
amistre64
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1/ln(2) is a constant; nothing changes about it ... so
amistre64
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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
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Ah, the 1/ln2 is a constant. Good insight. Thank you, @amistre64.
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what is a stick note?
amistre64
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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 :)
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okay, got it.
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I think the key to this one for me was recognizing that constant.
amistre64
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yep
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Would I then use the product rule against the remaining terms x^2 and ln(x^2+1) ?
amistre64
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i would, seeing how its a product ;)
FreeTrader
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Sometimes all the new stuff to learn can create uncertainty of the obvious.
amistre64
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yeah, im dong that with existence and uniquenes thrms right now wondering what gppd to do and stuff
amistre64
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good to do and stuff ... cant type
FreeTrader
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What class are you taking at this time?
amistre64
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im in college going to take linear algebra, calc3, and diffy qs in the spring
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I am taking Calc 1.
FreeTrader
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And reviewing precalc daily!
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Thanks, best wishes.
amistre64
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good luck :)