Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

what is a stick note?

Answer 9

sticky note is what thats spose to be, a post it note, something to remind you not to forget about it in the end :)

Answer 10

okay, got it.

Answer 11

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

Answer 12

yep

Answer 13

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

Answer 14

i would, seeing how its a product ;)

Answer 15

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

Answer 16

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

Answer 17

good to do and stuff ... cant type

Answer 18

What class are you taking at this time?

Answer 19

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

Answer 20

I am taking Calc 1.

Answer 21

And reviewing precalc daily!

Answer 22

Thanks, best wishes.

Answer 23

good luck :)