Theorem 3.4.1. Chain Rule.
If \(g\) is differentiable at \(x\) and \(f\) is differentiable at \(g(x)\text{,}\) then \((f(g(x))'=g'(x)f'(g(x))\)
Section 3.4 Chain Rule
The derivative has one more, arguably more fundamental, basic property that is generally referred to as the chain rule.
Let’s try it out.
\begin{equation*}
\begin{array}{llll}
(sin(x^2))' \amp = \amp (x^2)'sin'(x^2) \amp (\text{from the chain rule}) \\
\amp = \amp 2xcos(x^2) \amp (\text{known derivatives}) \\
\end{array}
\end{equation*}
