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How are gradients calculated in backpropagation for complex, long neural networks

I understand how to find the partial derivatives for the backpropagation algorithim but I have no idea how to implement it into code once there are multiple hidden layers and it gets impssible to keep track of the partial derivatives by hand. I am very confused on how you would keep track of the values as you go down layer by layer and I have not yet seen a resource that explains the backprogagation algorithim. Could someone explain this or point me to an appropriate resource. I am a beginner and I am trying to build a neural network from scratch but this is turning out to be difficult to wrap my head around as it is longer than I can keep track of and I do not know how to implement in code.