# Curvilinear coordinate, derivative

1. Oct 8, 2015

2. Oct 8, 2015

### Geofleur

It might help to look at a specific example, and 2D polar coordinates is a good one to start with. Take $u_1 = r$ and draw a picture of $\frac{\partial \mathbf{r}}{\partial r}$ at some point. It points radially away from the origin. Now note that surfaces of constant $r$ are just circles centered at the origin. The gradient is indeed normal to each such surface at the appropriate points.