Hi @gigaGPT
In this image show that the backpropagation step using computation graph help us in optimize our parameters using efficient way as we compute the derivative of \frac{\partial J}{\partial d}, and \frac{\partial J}{\partial a} only once and use it to calculate or the drivatives of our parameters whatever their number in our example is 2 (\frac{\partial J}{\partial w},\frac{\partial J}{\partial b}) so the calculation is much less is N+P calculations
But If you will choose any other optimization technique[brute force technique] this will cost you this number (N*P)calculations
Best Regards,
Abdelrahman