$\huge \begin{align} \epsilon &= \sum_{i=1}^{n}(a+bx_{i}-y_{i})^{2} \\ \pderiv{\epsilon}{a} &= \sum_{i=1}^{n}{ 2(a+bx_{i}-y_{i}) \\ } \\ &= 2(na + b \sigma_{x}- \sigma_{y}) \\ \pderiv{\epsilon}{b} &= \sum_{i=1}^{n}2x_{i}(a+bx_{i}-y_{i}) \\ &= 2(a \sigma_{x} + b\sigma_{x x} - \sigma_{xy}) \end{align}$