Propose an approach to extend your existing neural network model for computing these partial derivatives without requiring significant modifications or retraining. Explain the benefits and tradeoffs.

Use backpropagation to propagate gradients through the network, allowing us to compute partial derivatives with respect to each input feature. This can be achieved by modifying the forward pass to output not only the predictions but also the intermediate activations. Then, use backpropagation to back-calculate these partial derivatives. Benefits: no need for retraining or significant modifications; tradeoffs: increased computational costs due to additional forward passes and storage requirements.