# Differentiating vector function [Mathematica]

1. Jun 7, 2013

### Phudge

Hi.
So I have this vector function which I need to differentiate, it is however very tricky to do by hand, so I'm doing it in Mathematica.
$$\hat{u}=\left\langle\bar{u}+\bar{r}\frac{(1+\gamma)}{r(r+\bar{u}\cdot \bar{r})}\right\rangle$$
(The brackets denote normalisation)

I want to do this differentiation for the different components of r but first I want to show:

$$\frac{\partial\hat{u}}{\partial\gamma}=(\bar{r}-\bar{u}(\bar{u}\cdot\bar{r})\frac{1}{r(r+\bar{u}\cdot\bar{r})}$$
which I know to be correct from the paper I am basing my work on.
So my question to you guys is, how would I show that equality in Mathematica?

2. Jul 8, 2013

### djelovin

How come that there is no gamma dependence in you derivation?