Ytukyg

I'm trying to compute the gradient of a complex loss function but I'm stuck on calculating the derivative of part of the expression,namely:

with respect to $w_i$

$$sum_{n=1}^N(y^n -w_0 - sum_{j=1}^p A_{nj}w_j)^2$$

A - design matrix;
w - vector; y - vector; $w_0$ - first element of w

Edit
Where it said k it should have been n - now fixed

For $iin{1,ldots,p}$:

$$begin{align*}&phantom{=} , frac{partial}{partial w_i}sum_{n=1}^Nleft[left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)^2right]\
&=sum_{n=1}^Nfrac{partial}{partial w_i}left[left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)^2right]\
&=sum_{n=1}^Nleft[2left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)frac{partial}{partial w_i}left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)right]\
&=sum_{n=1}^Nleft[2left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)left( -sum_{j=1}^p A_{nj}frac{partial w_j}{partial w_i}right)right]\
&=sum_{n=1}^Nleft[2left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)left( - A_{ni}right)right]\
&=-2sum_{n=1}^Nleft[A_{ni}left(y^n -w_0 - sum_{j=1}^p A_{nj}w_jright)right]
end{align*}$$