Gradient Descent

$\displaystyle \frac{\partial E}{\partial w_{i}}$	=	$\displaystyle \frac{\partial}{\partial w_{i}} \frac{1}{2}\sum_{d}(t_{d} - o_{d})^{2}$
	=	$\displaystyle \frac{1}{2}\sum_{d}\frac{\partial}{\partial w_{i}} (t_{d} - o_{d})^{2}$
	=	$\displaystyle \frac{1}{2}\sum_{d} 2 (t_{d} - o_{d}) \frac{\partial}{\partial w_{i}}(t_{d} - o_{d})$
	=	$\displaystyle \sum_{d} (t_{d} - o_{d}) \frac{\partial}{\partial w_{i}}(t_{d} - \vec{w} \cdot \vec{x_{d}})$
$\displaystyle \frac{\partial E}{\partial w_{i}}$	=	$\displaystyle \sum_{d} (t_{d} - o_{d}) (- x_{i,d})$