Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

log power rule,

log (x^a) = a*log(x)