Do I need this capacitor ?

Yes, the DC bias points at each end are in general different, and will vary with the devices.
Carefully selected devices could possibly be made to work without C2, R5, and R6.
 
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your design is to open ended where is the input and where is the output
You have to give these before you will get a meaningful answer
Sorry to be so pedantic but we ca assume nothing if it is as i suspect you can get rid of the cap but as stated at present the design is meaningless
Trev
 
Frederico
Please do not think I am being difficult
the design can be re worked and made dc coupled i would only use a capacitor if i wanted to band limit i.e. reduce the bass response What do you want your circuit to do !
I have over 50 years in audio electronics but I do understand we all have to make a start even the longest journey has a first step
Is this just s design exercise I as an engineer like to make the simplest solution with the minimum of parts/ cost that does the job 100 %
best regards Trev