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Can someone explain this to me? In the above case ct=yt-gt

I tried to solve it as a three variable taylor approximation but got a few extra terms that weren't included in the above. So I am a little confused now.

I only need to understand how the first line was derived because I get additional terms with (gt-g)(chit-chi)..https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xap1/v/t35.0-12/13570139_10210195219259688_119153535_o.png?oh=5a83810acd11160ed4bf6a19de37d6ec&oe=57781CBB&__gda__=1467485097_6da652cc9db77ba174ecad977bc59004