- #1

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- 2

## Homework Statement

Start from the 'relevant equation' below and derive

$$ (1) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{j}}={\hat{q}}_{i}\frac{1}{{h}_{i}} \frac{\partial{h}_{i}}{{\partial{q}}_{j}}, {i}\ne{j}$$

$$ (2) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{i}}= -\sum {\hat{q}}_{j}\frac{1}{{h}_{j}} \frac{\partial{h}_{i}}{{\partial{q}}_{i}}, {j}\ne{i} $$

## Homework Equations

$$ \frac{\partial{\bf{r}}}{{\partial{q}}_{i}}={h}_{i}{\hat{q}}_{i} $$

## The Attempt at a Solution

I have finished the first part, using $$ \frac{\partial{\bf{\hat{r}}}}{{\partial{q}}_{j}}={h}_{j}\hat{q}_{j} $$

But I am not getting anywhere with part 2), especially with the summation ... a hint or 2 would be much appreciated please