I have a field : $\phi(x^\mu+\delta x^\mu)$.
Where $x^\mu$ is a quadriposition.
In my course we wrote :
$$ \phi(x^\mu+\delta x^\mu) \approx \phi(x^\mu)+\delta x^\mu \partial_\mu \phi(x^\mu)$$
What I don't understand is that we will have a "minus" sign that will occur for this taylor developpment.
$$ \phi(x^\mu+\delta x^\mu) \approx \phi(x^\mu)+[\delta x^0 \partial^0 -\delta x^i \partial^i ]\phi(x^\mu)$$
Can you help me to understand this ?