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.