DIFFERENTIAL COEFFICIENTS. 45 



. . , a-\-bx 



(4) = log j . 



6 a -bx 



-r, , a + bx 



Put T-= Z > 



a bx 



, c dz b (a - bx) + 1 (a + bx) . 



therefore -y- = ^ J- = = '- Art. 31, 



dx (a oxy 



. ,, cLy l &Q/D Ado 



therefore -/ = - - ^-^ = ^ T^ . 



dx z (a ox) a ox 



This example may also be solved by putting 

 y = log (a + bx) - log (a - bx), 



, , dy b b 2ab 



therefore -f- = j -\ ? = -= 7^-5 . 



dx a + bx a ox a ox 



(5) y = cos 



it- 

 Put 



3? 



therefore y = cos" 1 z, 



, dy _ dy dz ' 



dx dz dx' 



Now ^ = _- 77 _i__, Art. 66, 



. 

 " 



da_-Ga?-^-*-~~^ ^^ 31> 

 _3(^-4). 



