EXAMPLES OF SUCCESSIVE DIFFERENTIATION. 67 



21. Find the 4 th differential coefficient of -j - and of e"*?. 



6 \_ 



Results 



e x 4-] -\(f x j.ll/^.Lp 4 * 1 



' _'- - and e-**{Wx--lUx 



22. d " (ff> = {^c n + 2nxc n ~ l + n(n- 1) c"' 2 ) a* 



dx 



where c = log a. Art. 80. 



23. If y sin (m sin" 1 x) , shew that 



Apply Leibnitz's theorem, Art. 80, and deduce 



24. If y = a cos (log a;) + 5 sin (log a;), shew that 

 d 2 y du 



andthat 



F2 



