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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