Derivative of log proof question

[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?

 

[Dick]

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?

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

 

[LearninDaMath]

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

cool thanks