# How do you differentiate #f(x)=cotx/(1-sinx)#?

We can use the quotient rule:

where

and

or

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To differentiate ( f(x) = \frac{\cot(x)}{1-\sin(x)} ), use the quotient rule:

[ f'(x) = \frac{u'v - uv'}{v^2} ]

where ( u = \cot(x) ) and ( v = 1 - \sin(x) ). Differentiating ( u ) and ( v ):

[ u' = -\csc^2(x) ] [ v' = -\cos(x) ]

Substituting into the quotient rule formula:

[ f'(x) = \frac{(-\csc^2(x))(1-\sin(x)) - (\cot(x))(-\cos(x))}{(1-\sin(x))^2} ]

Simplify the numerator and denominator.

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