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## FreeTrader 3 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

$f(x) = x^2\log_{2} (x^2+1)$

2. amistre64

the log2 is best viewed as ln(x^2+1)/ln(2)

3. amistre64

since 1/ln(2) is a constant, all thats left is to consider this as a usual ln(u) type issue

4. FreeTrader

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

1/ln(2) is a constant; nothing changes about it ... so

6. amistre64

remove it, stick it to the side, put a stick note on top ot it and work the rest of the problem

7. FreeTrader

Ah, the 1/ln2 is a constant. Good insight. Thank you, @amistre64.

8. FreeTrader

what is a stick note?

9. amistre64

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

okay, got it.

11. FreeTrader

I think the key to this one for me was recognizing that constant.

12. amistre64

yep

13. FreeTrader

Would I then use the product rule against the remaining terms x^2 and ln(x^2+1) ?

14. amistre64

i would, seeing how its a product ;)

15. FreeTrader

Sometimes all the new stuff to learn can create uncertainty of the obvious.

16. amistre64

yeah, im dong that with existence and uniquenes thrms right now wondering what gppd to do and stuff

17. amistre64

good to do and stuff ... cant type

18. FreeTrader

What class are you taking at this time?

19. amistre64

im in college going to take linear algebra, calc3, and diffy qs in the spring

20. FreeTrader

I am taking Calc 1.

21. FreeTrader

And reviewing precalc daily!

22. FreeTrader

Thanks, best wishes.

23. amistre64

good luck :)

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