Three things:

1. Latex is currently down.

2. Use instead of

3. Your derivatives are a bit off.

Given z = sin(x + sin(t))

(del z)/(del x) = cos(x + sin(t)) *1

not cos(x + sin(1)).

This is the only error I saw, though you kept doing it consistently. So your other partials are wrong as well.

-Dan