What is the derivative of ${cot}^{- 1} (x)$ $cot^-1(x)$ ?

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Answer 1 · 2018-06-09T17:23:29

$\frac{d y}{d x} = - \frac{1}{x^{2} + 1}$ $dy/dx=-1/(x^2+1)$

Let $y=arccot(x)$
then
$cot(y)=x$
so

$-csc^2(y)dy/dx=1$
$dy/dx=-1/csc^2(x)$

$dy/dx=-1/(1+cot^2(y))$

$dy/dx=-1/(1+x^2)$
since $cot(y)=x$

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