Question

what is the derivative of log(base 10)x?

Answer 1

You can write it in terms of the natural logarithm by the change of base formula: \[\log_b a = \frac{\ln a}{\ln b}\]

Answer 2

Got it! Thanks :)

Answer 3

The derivation is lengthy, however I will reproduce it if you need it.
Let log(base 10)x = y
\[\frac{dy}{dx}=\frac{1}{x}\log_{10} e\]

Answer 4

Surely the derivation isn't long at all..? \[\frac{d}{dx}\log_{10} x = \frac{d}{dx}\frac{\ln x}{\ln 10} = \frac{d}{dx}\frac{\log_{10} e}{x}\]

Answer 5

Oops no derivative sign on the last one!

Answer 6

I was referring to a derivation that includes a demonstation that
\[\frac{d(\log_{e} x)}{dx}=\frac{1}{x}\]

Answer 7

Ah okay :)

Answer 8

@kropot72 did you mean something like this? http://www.youtube.com/watch?v=yUpDRpkUhf4

Answer 9

@agent0smith Sort of :)