Evaluating gradiant of vector basis r in Spherical Co-ordinates

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If I were to define $\nabla$ in spherical polar co-ordinates:

$$ \nabla=\frac{\partial}{\partial{R}}{\vec{e}_R}+\frac{1}{R}\frac{\partial}{\partial{\theta}}{\vec{e}_{\theta}}+\frac{1}{R\sin{\theta}}\frac{\partial}{\partial{\phi}}{\vec{e}_\phi} $$

And the basis vector, $\vec{r}$ as:

$$ \vec{r}=R\sin\theta\cos\phi{\vec{e}_R}+R\sin\theta\sin\phi{\vec{e}_\theta}+R\cos\theta{\vec{e}_\phi} $$

How would I evaluate ${\nabla{\vec{r}}}$? I'm assuming at this point it should equal 1+1+1. I'm just struggling to get there.

For completeness, I am looking to evaluate:

$$ (\vec{A}\cdot{\nabla})\vec{r}=\vec{A} $$