The derivative of cscx is -cscx cotx. This can be obtained using different methods including the quotient rule. Using the quotient rule, we can rewrite cscx as 1/sin(x) and differentiate it as follows:
$$\frac{d}{dx}(\csc x) = \frac{d}{dx}\left(\frac{1}{\sin x}\right) = -\frac{\cos x}{\sin^2 x} = -\csc x \cot x$$
Therefore, the derivative of cscx is -cscx cotx.
