## Calculus: Early Transcendentals 8th Edition

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