EULER'S THEOREM ( Theorem , proof & some example ).

EULER'S THEOREM ::-
     Homogenous function of three variables  ::-
   Definition  ::- 
         If a function f (x,y,z) of three independent variables  x, y, z be such that  f ( tx,ty, tz ) =t^n f ( x, y, z ) for every  t (>0 ) ,then f (x, y, z ) is said to be a Homogenous function of degree n.
Theorem ::-
EULER'S THEOREM  on Homogenous function of three variables 
  State::-
              If a differentiable function u= f (x, y, z) be a Homogenous function of degree n in x, y, z having continuous partial derivatives  , then 
     

 Theorem 

●● THEOREM 2 

State::- If u is a differentiable Homogenous function of degree n in two independent variable x and y , and all partial derivatives of first and second orede are continuous,  then

,