Looking on the internet deeply has found these results:

both mutually influence each other is the most popular phrase on the web.

both of you mutually influench each other 10 results on the web	both mutually influence each other 118 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Nov 20, 2015 ... Think about both the individual agency (of change champions) and institutional structures and how they both mutually influence each other. Both mutually influence each other: production systems [...] require a minimal space infrastructure, whereas through the development. [...] of space infrastructure�... Mar 2, 2015 ... ... or paradoxical relationship with the evolution of laws, in which one is inextricably linked to the other and both mutually influence each other. May 16, 2012 ... Ethic rules within science closely echo those of societies, and both mutually influence each other. Clear and transparent ethic rules in�...

both of you mutually influench each other

10 results on the web

both mutually influence each other

118 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Nov 20, 2015 ... Think about both the individual agency (of change champions) and institutional structures and how they both mutually influence each other.
Both mutually influence each other: production systems [...] require a minimal space infrastructure, whereas through the development. [...] of space infrastructure�...
Mar 2, 2015 ... ... or paradoxical relationship with the evolution of laws, in which one is inextricably linked to the other and both mutually influence each other.
May 16, 2012 ... Ethic rules within science closely echo those of societies, and both mutually influence each other. Clear and transparent ethic rules in�...