Infinite number of identical charges r=a2^n

[SherlockHolmie]

Homework Statement

Homework Equations

V=k∑q/r
E=-dV/ds

The Attempt at a Solution

I found part A plenty fine, 2kq/a

From here, I thought that the derivative of -V would give me the electric field, giving -2kq/a^2, but that's not the answer according to what my professor sent. I'm wondering why the derivative doesn't work.

I know there's something about how E=-∇V, but I'm not completely sure how to take gradients to begin with, but from my understanding, gradient of a 2d function is just its derivative with respect to its only variable.

Thanks

 

[haruspex]

I thought that the derivative of -V would give me the electric field

The electric field is the derivative of the potential with respect to displacements from the location where you are measuring the potential. That is not the same as a. If you change a you change the whole layout of the charges.
So you need to find the field due to each charge and add those.