# Derivative of log proof question

1. Feb 29, 2012

### LearninDaMath

Proof

d/dx [log$_{b}x$] = d/dx (lnx/lnb) = 1/lnb d/dx(lnx) = 1/xlnb , when x>0

I think I see the constant multiple rule at work here, but why? Is it because 1/lnb is a constant, so it is "factored" out of lnx/lnb and treated as a constant while lnx is treated as the term to be differentiated?

2. Feb 29, 2012

### Dick

Exactly. ln(b) is just a constant factor, like 2.

3. Mar 1, 2012

cool thanks