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Derivative of the inverse cotangent
The first derivative of the inverse cotangent is
Explanation
We'll start with the cotangent, for which applies
and the inverse
Differentiation gives
To this we apply the chain rule
Turning over delivers
We want to trace this back to a function that only contains cot y, because we can then replace that with x. For the sake of clarity we write
With the fundamental formula of trigonometry we get
Division of the numerator and denominator by sin2y shows
Substitution of y = arccot x and cot y = x gives