For this specific model, with just one output node and two hidden nodes, the gradient descent equations take the following form for output layer
w_{i}^{(2)}\leftarrow w_{i}^{(2)}- \eta \delta^{(2)} a_{i}^{(1)},and
b^{(2)} \leftarrow b^{(2)}-\eta \delta^{(2)},and
w_{ij}^{(1)}\leftarrow w_{ij}^{(1)}- \eta \delta_{i}^{(1)} a_{j}^{(0)},and
b_{i}^{(1)} \leftarrow b_{i}^{(1)}-\eta \delta_{i}^{(1)},where \eta is the learning rate.