Answer
$\coth t$
Work Step by Step
Given: $F(t)=\ln{(\sinh t)}$
Now, $F'(t)=\dfrac{d}{dt}[\ln{(\sinh t)}]$
On applying the chain rule, we have
$F'(t)=(\dfrac{d\ln{(\sinh t)}}{d\sinh t})(\dfrac{d\sinh t}{dt})$
or, $=(\dfrac{1}{\sinh t})(\cosh t)$
or, $=\dfrac{\cosh t}{\sinh t}$
$=\coth t$
