Differential of Arccot x
To find\[\frac{d}{dx}(cot^{-1}x)\]
;et \[y=cot^{-1}x\]
then \[coty=x\]
.Differentiating implicitly gives
\[- cosec^2 x \frac{dy}{dx}=1 \rightarrow \frac{dy}{dx}=- \frac{1}{cosec^2 y}\]
.To express
\[\frac{dy}{dx}\]
in terms of \[x\]
use \[coty=x,\; cosec^2y =cot^2y+1=x^2+1\]
.Then
\[\frac{dy}{dx}=- \frac{1}{x^2+1}\]
.