$\frac{a \cos x + b \sin x + c}{\sin x}$

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Solution

$\frac{d}{d x} (\frac{a \cos x + b \sin x + c}{\sin x}) = \frac{d}{d x} (\frac{a \cos x}{\sin x}) + \frac{d}{d x} (\frac{b \sin x}{\sin x}) + \frac{d}{d x} (\frac{c}{\sin x}) = a \frac{d}{d x} (c o t x) + \frac{d}{d x} (b) + c \frac{d}{d x} (\cos e c x) = - a \cos e c^{2} x + 0 - c \cos e c x c o t x = - a \cos e c^{2} x - c \cos e c x c o t x$

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