Answer
$$f'(t)=\frac{2\cosh t}{(1-\sinh t)^2}$$
Work Step by Step
$f'(t)=\frac{d}{dt}\frac{1+\sinh t}{1-\sinh t}$
Using the quotient rule:
$f'(t)=\frac{\cosh t(1-\sinh t)-(1+\sinh t)(-\cosh t)}{(1-\sinh t)^2}$
$=\frac{\cosh t-\cosh t\sinh t+\cosh t+\cosh t\sinh t}{(1-\sinh t)^2}$
$=\frac{2\cosh t}{(1-\sinh t)^2}$
