Maxwells Equations being non-invariant with Galilean transformations

[Xyius]

I just purchased a book on the introduction of special relativity and I seem to be stuck on a simple mathematical step. For some reason I just can't see this!

This is what it says:

Although the general transformation above can be handled, we will
take its simplifed version in which O' is moving away from O along the
x-axis and O and O' coincided when t' = t = 0. It is easy to see that the
partial derivatives are related as follows:

$$\frac{∂}{∂x}=\frac{∂}{∂x'}$$
$$\frac{∂}{∂y}=\frac{∂}{∂y'}$$
$$\frac{∂}{∂z}=\frac{∂}{∂z'}$$

$$\frac{∂}{∂t}=\frac{∂}{∂t'}-v\frac{∂}{∂x'}$$

Gotta love getting stuck on something when the book says its "Easy to see." Confidence -1.

 

[jtbell]

The Galilean transformation in this case is x' = x - vt; y' = y; z' = z; t' = t.

Apply the chain rule for partial derivatives, e.g.

$$\frac{\partial}{\partial t} =
\frac{\partial x^\prime}{\partial t} \frac{\partial}{\partial x^\prime} +
\frac{\partial y^\prime}{\partial t} \frac{\partial}{\partial y^\prime} +
\frac{\partial z^\prime}{\partial t} \frac{\partial}{\partial z^\prime} +
\frac{\partial t^\prime}{\partial t} \frac{\partial}{\partial t^\prime}$$