Question

How do you find the derivatives of `s=lnroott(t)`?

Answer 1

`d/(dt) ( ln root (t)(t)) =(1- lnt)/t^2`

Explanation:

Using the properties of logarithms:

`s = ln root(t)(t) = 1/tlnt`

we can differentiate using the product rule:

`(ds)/(dt) = 1/t d/(dt) ln t + lnt d/(dt)(1/t)`

`(ds)/(dt) = 1/t 1/t + lnt (-1/t^2)`

`(ds)/(dt) = 1/t^2(1- lnt)`