Differential of Arccosech x

To find  
\[\frac{d}{dx}(cosech^{-1}x)\]
  let  
\[y=cosech^{-1}x\]
  then  
\[cosechy=x\]
.
Differentiating implicitly gives  
\[-cosechycothy \frac{dy}{dx}=1 \rightarrow \frac{dy}{dx}=- \frac{1}{cosechy cothy}\]
.
To express  
\[\frac{dy}{dx}\]
  in terms of  
\[x\]
  use  
\[cosechy=x,\; cothy = \sqrt{cosech^2y+1} =\sqrt{x^2+1}\]
.
Then  
\[\frac{dy}{dx}=- \frac{1}{x \sqrt{x^2+1}}\]
.

You have no rights to post comments