SPECIAL APPLICATION OF ANALYSIS l6l 



d n+l _ = 



9' +l S] 



. _ L = 1-3-5 . . . . (2- i) / x i /\ i -* 



] 2 n^ _ ^ n ^/ I _ X 2 \ 2W.-I \I / I + * 



i-3 M A - A 2 __ ^5 _ (n\ (l 



(2W - l)(2W - 3) \2/ \I + */ (2 - l)(2W - 3)(2 - 5) \3/ \I 



7.39 Derivatives of Implicit Functions. 

 7.391 If y is a function of x, and/0, >) = o. 



dy 



df 



" 



d?y _ \dy dx 2 " dx dy dxdy \dx 

 2 '^= /d/\ 



\dy/ 

 7.392 If 2 is a function of # and y, and /(x, y, z) = o. 



df 



dx dz 



_ 



' dx~ ' df' dy dj_ 



dz dz 



a a d df 



dz dx* 2 dx dx dxdz\dx/ dz\ 



(df\* 

 \dz) 



dfVVf dj dj d^_ WV ffi 

 a'z a 2 as dy dydz ^~ \dyj dz\ 



df 

 dz 



___ 

 d 2 z ( dz ) dxdy dz \dx dydz ^ dy dxdz/ dx dy dz* 



/^A 3 

 \dz 



