How to derive the gradient for SSE cost function in Adaline?

Question

I started learning machine learning and have some troubles in understanding derive rules for the gradient of cost function in particular I can't understand how sum(wjxj) transformed to -xj. I tried to google a detailed breakdown explanation but everywhere the same. I know that it pretty simple for mathematicians for those who hasn't met this for quite long time it's a problem.

Could someone explain or/and give links to some resources regarding that.

Thanks in advance!

Answer 1

I just wrote the first few terms on a sheet of paper and understood it. All other terms exept

w⁽ⁱ⁾_j * x⁽ⁱ⁾_j

are constant and thus derive to 0.

The

w⁽ⁱ⁾_j * x⁽ⁱ⁾_j

derives to

x⁽ⁱ⁾_j