Let and be functions such that is defined. If is differentiable at and is differentiable at , then is differentiable at and
Alternatively, if
then,
let
Since is differentiable at , the function is defined in a neighbourhood of 0.
Further, as . Now
Letting in the above, we get
Thus, for
Since is continuous at ,
Thus, from the above equation we get
and 
be functions such that 
is defined. If 
is differentiable at 
and 
is differentiable at 
, then 
is differentiable at 
and 
is differentiable at 
, the function 
is defined in a neighbourhood of 0. 
as 
. Now 
in the above, we get 
is continuous at 
, 
