TITLE: Differentiate.$ y = \frac{7x}{ 6 − \cot x}$
QUESTION [5 upvotes]: I have no idea what I have done wrong. Please criticise.

REPLY [3 votes]: You are just off by a negative sign. You say that you say $\frac{d}{dx} [6-\cot(x)]= -\csc^2(x)$, but it should be  $\frac{d}{dx} [6-\cot(x)] = \csc^2(x)$. This means you should get $$y' = \frac{42-7\cot(x)-7x\csc^2(x)}{(6-\cot(x))^2}$$ Does this match what you would expect?