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Backpropagation by hand

Given the computational graph above, we want to calculate the derivatives for the leaf nodes (x, y and z). To get you started we already calculated the results of the forward pass (in red) in addition to calculating the derivatives of f and q.

The rules for derivative computations have been given in the table below:

Interaction Overall Change
Addition \((f+g)' = f' + g'\)
Multiplication \((f \cdot g)' = f \cdot dg + g \cdot df\)
Powers \((x^n)' = \frac{d}{dx}x^n = nx^{n-1}\)
Inverse \((\frac{1}{x})' = - \frac{1}{x^2}\)
Division \((\frac{f}{g})' = (df \cdot \frac{1}{g}) + (\frac{-1}{g^2}dg \cdot f)\)
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