Differential of Arcsech x
\[\frac{d}{dx}(sech^{-1}x)\]
;et \[y=sech^{-1}x\]
then \[sechy=x\]
.Differentiating implicitly gives
\[-sechytanhy \frac{dy}{dx}=1 \rightarrow \frac{dy}{dx}=- \frac{1}{sechy tanhy}\]
.To express
\[\frac{dy}{dx}\]
in terms of \[x\]
use \[sechy=x,\; tanhy = \sqrt{1-sech^2y} =\sqrt{1-x^2}\]
.Then
\[\frac{dy}{dx}=- \frac{1}{x \sqrt{1-x^2}}\]
. 
