i checked with wikipedia, and it says:

$\displaystyle \Delta U= O(\delta T) + O((\delta X)^{2}) $

but in my question, it asks about order of error. Which order i should answer?

And I substitude $\displaystyle \frac{\delta U}{\delta T}=\frac{\delta^{2}U}{\delta X^{2}} $ and multiply both sides by $\displaystyle \delta T $ ,

I found the error should be : $\displaystyle O((\delta T)^{2}) + O((\delta T)(\delta X)^{2}) $

anyone can explain how the answer in wiki comes out?