The Chain Rule is one of the most powerful differential rules. Just like the {Limits →Composition of Limits and functions}, its versatility allows the differentiation of composition function whole lot easier.
$$ \frac d {dx}f(g(x))=f'(g(x))g'(x) $$
<aside> ⚙ There is a similar process of the Product Rule of Derivative; but however, there is also a basic concept/theorem to go over, before we go over the proof of the Chain Rule.
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If is a differentiable function of and is a differentiable function of then is a differentiable function of and
$$ \frac {dy} {dx} =\frac {dy}{du}\frac {du}{dx} $$
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from 2551, in this case y as dependent variable, and dx is the independent variable.
$$ \frac d {dx}f(g(x))=f'(g(x))\centerdot g'(x) $$