To differentiate the function [tex]\(-1 - \cot^2(x)\)[/tex] with respect to [tex]\(y\)[/tex], we need to consider how the function depends on [tex]\(y\)[/tex].
Given the function [tex]\( -1 - \cot^2(x) \)[/tex], it is important to note that the variables involved in the function are [tex]\(x\)[/tex] and not [tex]\(y\)[/tex]. Therefore, since the function does not contain the variable [tex]\(y\)[/tex], the differentiation of this function with respect to [tex]\(y\)[/tex] results in 0.
Thus, the derivative of [tex]\(-1 - \cot^2(x)\)[/tex] with respect to [tex]\(y\)[/tex] is:
[tex]\[ \frac{d}{dy} \left(-1 - \cot^2(x)\right) = 0. \][/tex]
