çalýþmak (as "to try") needs something -a: çalýþmaya çalýþacaðým

-  I´ll try to work: "çalýþmayý deneyeceðim"  or  "çalýþmaya gayret edeceðim"

--I´ll try my best :   "en iyisini yapmayý deneyeceðim" or "en iyisini yapmaya gayret edeceðim"

Thanks for the correction, you´re right it should be

- Çalýþmaya çalýþacaðým.

And yes, I realize - çalýþmayý deneyeceðim -  doesn´t mean I´ll try my best but saying - I´ll try working on it - doesn´t give quite the right meaning. Thanks for catching that though!