Error Gradient for a Sigmoid Unit

$$\frac{\partial E}{\partial w_{i}} \frac{\partial}{\partial w_{i}}\ \frac{1}{2}\sum_{d\in D}(t_{d} - o_{d})^{2}$$ =

$$\frac{1}{2}\sum_{d}\frac{\partial}{\partial w_{i}} (t_{d} - o_{d})^{2}$$ =

$$\frac{1}{2}\sum_{d} 2 (t_{d} - o_{d}) \frac{\partial}{\partial w_{i}}(t_{d} - o_{d})$$ =

$$\sum_{d} (t_{d} - o_{d}) \left( - \frac{\partial o_{d}}{\partial w_{i}}\right)$$ =

$$- \sum_{d} (t_{d} - o_{d})\ \frac{\partial o_{d}}{\partial net_{d}}\ \frac{\partial net_{d}}{\partial w_{i}}$$ =

But we know:

$$\frac{\partial o_{d}}{\partial net_{d}} = \frac{\partial \sigma(net_{d})}{\partial net_{d}} = o_{d}(1 - o_{d})$$

$$\frac{\partial net_{d}}{\partial w_{i}} = \frac{\partial (\vec{w} \cdot \vec{x}_{d})}{\partial w_{i}} = x_{i,d}$$

So:

$$\frac{\partial E}{\partial w_{i}} - \sum_{d \in D} (t_{d} - o_{d}) o_{d}(1-o_{d}) x_{i,d}$$ =