A calculus of the absurd

10.5 The chain rule

The chain rule is used to find the derivatives of "functions of a function". Mathematically, these are written as

\[\frac {d}{dx}[y(u(x))]\]

and it’s possible to find this just by known the derivatives of \(y(u)\) and \(u(x)\).

The proof is a little involved, so for the moment you can find it at http://kruel.co/math/chainrule.pdf.

The result we’re after is that

\begin{equation} \frac {dy}{dx} = \frac {dy}{du} \frac {du}{dx} \end{equation}