Answer
$f'(t)=\dfrac{2\cosh t}{(1-\sinh t)^2}$
Work Step by Step
Given: $f(t)=\dfrac{1+\sinh t}{1-\sinh t}$
Now,$f'(t)=\dfrac{d}{dt}[\dfrac{1+\sinh t}{1-\sinh t}]$
Apply the quotient rule, we get
$f'(t)=\dfrac{\cosh t(1-\sinh t)-(1+\sinh t)(-\cosh t)}{(1-\sinh t)^2}$
or, $f'(t)=\dfrac{\cosh t-\cosh t\sinh t+\cosh t+\cosh t\sinh t}{(1-\sinh t)^2}$
or, $f'(t)=\dfrac{2\cosh t}{(1-\sinh t)^2}$
