Chain Rule

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

For example,
if Hunger = H, Time = t, Crave Ice Cream = Ice and
$$
H = t^2 + \frac{1}{2}
$$
$$
Ice = sqrt(H)
$$
Then,
$$
\begin{align*}
\frac{\partial H}{\partial t} &= \frac{\partial}{\partial t} (t^2 + \frac{1}{2}) \\&= 2t + 0 \\&= 2t
\end{align*}
$$
And,
$$
\begin{align*}
\frac{\partial Ice}{\partial H} &= \frac{\partial}{\partial H} \sqrt H \\&= \frac{1}{2 \sqrt H}
\end{align*}
$$
So,
$$
\begin{align*}
\frac{\partial Ice}{\partial t} &= \frac{\partial Ice}{\partial h} * \frac{\partial H}{\partial t} \\&= \frac{1}{2 \sqrt H} * 2t \\&= \frac{t}{\sqrt H}
\end{align*}
$$