Second order Taylor approximation

[tanvi nautiyal]

Hello,
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

 

[Ssnow]

In fact in the Taylor expansion you have also the terms $u_{G}(G_{t}-G)$ and $u_{\zeta}(\zeta_{t}-\zeta)$ but in the formula doesn't appear, I think there are some assumptions that permit to put zero these terms ...

PS. $\zeta$ is not chi that is $\chi$

 

[chiro]

Hey tanyi nautiyal.

Can you please re-attach the image so we can have a look at it?