## anonymous one year ago having a mental skid... how do you calculate by hand the derivative for Log [1/x] ?

1. anonymous

I know Log[x] --> 1/x but it cant be 1/(1x) can it?

2. jim_thompson5910

if the log is base e, ie a natural log, then log(1/x) = log(x^(-1)) = -1*log(x) then you would derive that to get -1/x

3. anonymous

yes thats the base .. ahh right on.. extract the -1 via the exponent.

4. anonymous

does it help to know that $\log(\frac{1}{x})=-\log(x)$

5. anonymous

yes they both help.. thanks... whats the name of that identity there satellite?

6. dan815

log power rule, log (x^a) = a*log(x)