Suppose we have two inertial frames O and O', with O' moving along the positive axis of O with a uniform speedSuppose we have a functionin O'. The total derivative ofis

But

and with

so

and similarly

and withso and

Hence

Regrouping gives

Hence

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Suppose we have two inertial frames O and O', with O' moving along the positive axis of O with a uniform speedSuppose we have a functionin O'. The total derivative ofis

But

and with

so

and similarly

and withso and

Hence

Regrouping gives

Hence