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What does the chain rule for differentiation state?
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If $y=f(u)$ is a differentiable function of $u$ and $u=g(x)$ is a differentiable function of $x$, then $y=f[g(x)]$ is a differentiable function of $x$ and

$\frac{d y}{d x}=\frac{d y}{d u} \times \frac{d u}{d x} \quad$ or equivalently, $\quad \frac{d y}{d x}=y^{\prime}=f^{\prime}[g(x)] g^{\prime}(x) .$

In applying the Chain Rule, think of the opposite function $f^{\circ} g$ as having an inside and an outside
part:

$$y=f \underbrace{[g(x)]}_{u=g(x) \atop \text { inside }}=\underbrace{f(u)}_{\text {outside }}$$
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