Chain Rule

Chain rule is used to differentiate a variable which is depended on another variable.

Back Propagation applies the chain rule through a network to compute Gradients; it is a core rule of Differentiation.

For example,
if Hunger = H, Time = t, Crave Ice Cream = Ice and

H = t^{2} + \frac{1}{2}

I c e = s q r t (H)

Then,

\begin{aligned} \frac{\partial H}{\partial t} & =\frac{\partial}{\partial t}(t^{2}+\frac{1}{2}) \\ =2t+0 \\ =2t \end{aligned}

And,

\begin{aligned} \frac{\partial I c e}{\partial H} & =\frac{\partial}{\partial H}\sqrt{H} \\ =\frac{1}{2 \sqrt{H}} \end{aligned}

So,

\begin{aligned} \frac{\partial I c e}{\partial t} & =\frac{\partial I c e}{\partial h}*\frac{\partial H}{\partial t} \\ =\frac{1}{2 \sqrt{H}}*2t \\ =\frac{t}{\sqrt{H}} \end{aligned}

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