Chain Rule

A representation of Chain Rule from Deep Learning from Scratch - Pasted image 20231203184705 (Image source: Deep Learning from Scratch by Mr Seth Weidman)

Assume two functions \(f_{1}(u) \text{ and } f_{2}(u)\).
Consider the composite function \(f(u) = f_{2}(f_{1}(u))\).

Chain Rule mathematically states: The derivative of the composite function \(f\) at a value \(x\) will be the product of the derivative of \(f_1\) at \(x\) times the derivative of \(f_2\) at \(f_1(x)\):

\[\frac{df_{2}}{du}(x) = \frac{df_{2}}{du}(f_{1}(x)) \times \frac{df_{1}}{du}(x)\]
Last update : 25 mai 2024
Created : 25 mai 2024