independently
US /ˌɪn.dɪˈpen.dənt.li/
UK /ˌɪn.dɪˈpen.dənt.li/

1.
without being influenced or controlled by others in matters of opinion, conduct, etc.
:
•
She decided to live independently after college.
•
The two teams worked independently on the same problem.
2.
without connection with each other; separately
:
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The results were obtained independently by two different labs.
•
These two events occurred independently of each other.