110 EXAMPLES OF INDEPENDENT DIFFERENTIATIONS. 



10. If u = tan" 1 .. Xy .. - F , shew that 



* ' 



dxdy 

 11. If u = 



shew that 



12. If M = log (x s + y s + 2 s - Zxyz), shew that 

 1 d 3 u 1 du du du 



6 dx dy dz 3 dx dy dz 



du du du _ 3 

 dx dy dz 



t 

 ? dy" dz* dx dy dy dz dz dx 



d?u d*u 360 



I ~~7 3 ~1 S 7~ "1 7 -2 7 S 7~~~ 



C?M d*u d?u __ 3 



?M 72 



__ 



"I T s~T" "i 



dx*ciydz dxdy s dz dxdydz* (x + y + z) 6 



