Logarithmic Differentiation

1. Apr 6, 2005

huan.conchito

Can someone please differentiate this $\!\(Log\\_2\[[x^3 + 1]$
im stuck because its base 2

2. Apr 6, 2005

Moo Of Doom

Remember that $$\log_a{x}=\frac{\log_b{x}}{\log_b{a}}$$

3. Apr 6, 2005

huan.conchito

so is this my next step? and then do i use quotient rule?
$$\log_2{(x^3+1)}=\frac{\ln{(x^3+1)}}{\ln{2}}$$

4. Apr 6, 2005

Moo Of Doom

You don't need the quotient rule because ln2 is a constant.

5. Apr 6, 2005

huan.conchito

so is the the answer then?
$3x^2/(x^3+1)$

6. Apr 6, 2005

Hurkyl

Staff Emeritus
He used the chain rule just fine.

He just forgot how to deal with a constant multiple. Hint: what's the derivative of 6 x^2?

7. Apr 6, 2005

huan.conchito

ah, thanks
$3x^2/(x^3+1)Ln2$

8. Apr 6, 2005

dextercioby

And $\ln 2$ should be there somewhere.In the denominator,to be precise.

And the thread title,to be accurate,should have been "logarithm('s) derivative"...

Daniel.

9. Apr 6, 2005

SpaceTiger

Staff Emeritus
I deleted my response because he changed his post before I submitted, or it displayed incorrectly on my browser.