# The chain rule: if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x)
# 
# For our network: Loss = MSE(sigmoid(W2 * sigmoid(W1 * X + b1) + b2), y)
# We need: dLoss/dW2, dLoss/db2, dLoss/dW1, dLoss/db1

print("Chain rule breakdown:")
print("dLoss/dW2 = dLoss/da2 * da2/dz2 * dz2/dW2")
print("  where:")
print("    dLoss/da2 = 2 * (predictions - targets)  # MSE derivative")
print("    da2/dz2 = sigmoid'(z2)                   # sigmoid derivative")
print("    dz2/dW2 = a1                             # linear layer derivative")