Question

What is the derivative of cot-1 (x)?

Answer 1

cot-1(x) = y

x = cot(y)

and its worked from that angle

Answer 2

or start with
\[\cot(\cot^{-1}(x))=x\] and use implicit diff to find the one you want. it is always true that
\[f^{-1}(x)'=\frac{1}{f'(f^{-1})}\]