Chain rule question (differential termination)

Why is the following equation true? given: $ x '= x + vt $,
$ frac { partial} { partial x } = frac { partial x} { partial x } frac { partial} { partial x} + frac { partial t } { partial x } frac { partial} { partial t} $,
If that were not 1 = 2, if you can pick up the differentials (z. $ frac { partial x} { partial x} = 1 $)