Gradient of scalar product of constant and position vector (index notation)

Question

I'm just getting comfortable with the use of index (Einstein) notation, but having not dealt with vectors for a couple of years I'm a little stuck.

For the following problem:

$$\bar \Delta (\bar c \cdot \bar r)$$

Where $\bar c$ is a constant vector and $\bar r$ is a position vector.

The solution to the problem is :

$$\bar c$$

I thought that the first line of working might be:

$$\partial_i (c_j r_j)_i$$

But I'm not sure if this is to correct...or what to do next.

Thanks in advance for your help!

Answer 1

I know the answer so I thought I'd put it in for any Googlers.

$$ \bar \Delta (\bar c \cdot \bar r)$$

LHS:

$$ d_i (c_j r_j) $$

$$ = c_j \delta_{ij} $$

$$ = c_i $$

$$ = \bar c$$