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

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Answer 1 · 2017-01-10T18:39:13

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

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

$s(t) = -tlnt$

and differentiate using the product rule:

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

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