88 PRACTICAL MATHEMATICS 



dy dy dz 

 dx dz dx 



= nz n ~ l cos x 



= n sin* 1 " 1 x cos x 



(2) To differentiate e?^ 1 * 



Then y = & where z = sin" 1 x 



dy , dz 1 



-/ = e* and -j- = . 



dz da; y i a; 2 



d?/ dy dz 

 * 



Vl-a; 2 



gsin- 1 *! 



(3) To differentiate tan- 1 x z 



Then y = tan* 1 z where z = x z 



dz 1 + 

 dy_dy dz_ 

 dx~ dz x dx 



1+ z 2 



(4) To differentiate log,(a + bx + cx z ) 



Then y = log e z where z = a + bx + cx z 



dy I , dz , 



-r = - and -r- = o + 2c 



dz z oa? 



dw dw dz 



But -/ = ^ x -T- 



da? dz cte 



a + bx + cx z 



