Question

How do you find the derivatives of `s=ln(t^-t)`?

Answer 1

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

Explanation:

Considering that : `ln ( t^alpha) = alpha ln t` we can rewrite the function as:

`s(t) = -tlnt`

and differentiate using the product rule:

`d/(dt) s(t) = -t d/(dt)(ln t) -lnt (dt)/(dt) = -t *1/t -lnt = -lnt-1`