OF THE INVERSE TRIGONOMETRICAL FUNCTIONS. 39 



66. Differential coefficient ofcos~ l x. 

 Let y = cos^x, therefore 



cosy = x, 



fjni* 



therefore -r- = sin y, Art. 52, 



therefore - = , Art. 60, 



ax sin y 



1 



See the preceding Article. 



67. Differential coefficient of tan" 1 a; and cottar. 

 Let y = ta,u~ l x, therefore 



x = tan y, 

 dx 1 



Similarly, if y = cot 1 x, 



% = __1 

 dx 1 + a; a * 



68. Differential coefficient of sec' 1 a; 

 Let y = sec~ 1 x, therefore 



x = sec y, 



dx siny . 



therefore -*- = f- , Art. oo, 



ay cos y 



filf OOS 7/ 



therefore -/".-> Art. 60. 



