Differential of asrcsec x

To find  
\[\frac{d}{dx}(sec^{-1}x)\]
 ;et  
\[y=sec^{-1}x\]
  then  
\[secy=x\]
.
Differentiating implicitly gives  
\[secytany \frac{dy}{dx}=1 \rightarrow \frac{dy}{dx}= \frac{1}{secy tany}\]
.
To express  
\[\frac{dy}{dx}\]
  in terms of  
\[x\]
  use  
\[secy=x,\; tany = \sqrt{sec^2y-1} =\sqrt{x^2-1}\]
.
Then  
\[\frac{dy}{dx}= \frac{1}{x \sqrt{x^2-1}}\]
.

Add comment

Security code
Refresh