<p>This question really stumped me</p>
<p>p(t)=t^(1/t)
find p'(t).</p>
<p>Can anyone figure this one out?</p>
<p>What you have to do is take the natural logarithm of both sides before differentiating. So you get:
ln(p(t)) = (1/t)lnt
taking d/dx(ln(p(t)) = d/dx((1/t)lnt) gets you:
(1/p(t))p'(t) = (1/t)(1/t) - (1/t^2)(lnt)
so
p'(t)/p(t) = (1 - lnt)/t^2
and
p'(t) = ((1 - lnt)/t^2)(t^(1/t))</p>
<p>Hey thanks!</p>
<p>I was trying to use the chain rule, but it didn't work out to well</p>
<p>-Rootbeer</p>