# Help on differentiation of tensor fields

1. Jan 12, 2008

### erkokite

Given a tensor field T(x,y,z), how would I go about differentiating it wrt spacial coordinates?

I would presume that it would work like this:

$$\frac{\partial T}{\partial x} = \lim_{h\to 0}\frac{T(x+h,y,z)-T(x,y,z)}{h}$$

However, this does not seem to take into account that tensor quantities themselves can act as functions of the spacial coordinates. My understanding is that a tensor field can, in some instances, act like a field that returns functions (or maps). If T returns tensors that are dependent on x, y, or z, wouldn't this have to be taken into account? Or is that another type of differentiation?