Saturday, October 11, 2008

`h(t) = ln(t)/t` Find the derivative of the function.

We'll
use the formula of the derivative of a quotient:  `(u/v)' = (u'v-u v')/v^2.`  Here u=`ln(t)` and
`v=t,` therefore `u'=1/t` and `v'=1.` So

`h'(t) = (1/t *t - ln(t))/t^2 = (1 -
ln(t))/t^2.`

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