Exponential Functions
Two extra tricks need to be kept in mind when dealing with exponential functions.
e^{nx} = (e^{x})^{n}
e^{a + b} = (e^{a})(e^{b})
Example 5 

4xe^{2x} 8e^{x} 
Strategy 
4xe^{2x} and 8e^{x} 
Consider each product separately,
but watch out for sums which may be in common 
4 and 8 have a HCF of 4 
Find the highest common factor
of the numeric parts of the product expressions. 
x is in only one term 
Find the common factor for
factors involving a variable. 
Since e^{2x} = (e^{x})^{2}
e^{2x} and e^{x} have e^{x} in common 
Find the common factor for factors which involve exponential factors. 
Hence 4e^{x} is the largest common
factor. 

4xe^{2x} 8e^{x}
= 4e^{x}(xe^{x})
+ 4e^{x}(2)
= 4e^{x}(xe^{x}
+ 2) 
Put the parts together. 
Here are some exercises to finish off:
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