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  
\[\frac{dy}{dx}=- \frac{1}{x^2+1}\]
.

You have no rights to post comments