MacLaurin series of Exponential function, 
The MacLaulin series (Taylor series at 
) representation of a function 
is 
The derivatives of the exponential function
and their values at are: 
Note that the derivative of
is also and 
. We substitute this value of 
in the above MacLaurin series: 
We can also get the MacLaurin series of
by replacing 
to 
: 
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