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Derivative of the inverse cosecant
The first derivative of the inverse cosecant is
Explanation
We start with
Differentiation gives
Now we apply the chain rule
Turning over delivers
We want to trace this back to a function that only contains csc y, because we can then replace that with x, and in the conversion table we find
Substitution of y = arccsc x and csc y = x gives then
and for real x applies