/sci/ - Science & Math

Consider the parametrization [math]\mathbf{r} = R \mathbf{e}_r + \phi \mathbf{e}_\phi + \theta \mathbf{e}_\theta [/math] in spherical coodinates. When I partially differentiate this parametrization wrt theta, do I get
>[math]\frac{\partial \mathbf{r}}{\partial \theta} = (1+R)\mathbf{e}_\theta - \theta \mathbf{e}_r [/math]
Looks wrong to me, but all I did was applying product and chain rule when differentiating the spherical basis vectors. So I don't see where my mistake is.