## Calculus 8th Edition

$\coth t$
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, $=\dfrac{\cosh t}{\sinh t}$ $=\coth t$