Answer
Differentiate $y=\frac{\cos x}{1-\sin x}$
$y'=\frac{1}{1-\sin x}$
Work Step by Step
Differentiate using the quotient rule and the trig rules.
$y'=\frac{-\sin x(1-\sin x) - \cos x(-\cos x)}{(1-\sin x)^2}$
$=\frac{-\sin x + \sin ^2x + \cos ^2 x}{(1-\sin x)^2}$
Simplify the top using the trig identities.
$=\frac{1-\sin x}{(1-\sin x)^2}$
$=\frac{1}{1-\sin x}$