EXAMPLES OF ELIMINATION. 277 



13. If log z = (f> (ay + bx)+^ (ay - Ix), then 

 dz 



^ \ Tt X+U J. f \ At. UH US Z 



14. It z = e "<b (x + y), then -= -^- = . 



dx dy x+y 



15. If z tj> (e* sin y), then sin y -j- = cos y -j- . 



^ /^V- 2 -^- -i- /" Y - o 



a a; dy dy* \dx) 



17. 



x mz 



, dz , * dz 



18. Eliminate the arbitrary functions from 



z = x$ (ax + by] + yty (ax + by}. 



n 7^ 2^2 ^ r d* z . ud*z . 

 Result, a* -j- z - 2ab -jj- + o 2 ^- 2 = 0. 



' * 



19. Eliminate the arbitrary and exponential functions from 



' 7i c? 2 w , , du , d*u 

 Result, -j-f = n w + 2w j- + -j-j. 

 ax ay ay 



20. Eliminate the circular and logarithmic functions from 

 (1) y = sin logic, (2) y = log sin a;. 



. (i) *' + * + y=o, ( 2 ) ! 



