Chain rule
lastmod 2018-08-17created 2015-12-281 edits
The chain rule is a formula for the derivative of a composite function formed by composing two functions.
\[ (f \circ g)'(x) = (f(g(x)))' = f'(g(x)) g'(x) \]
In Leibniz notation, it is as follows.
\[ \frac {df}{dx} = \frac {df} {dg} \cdot \frac {dg}{dx} \]
It can be proved simply using Carathéodory's lemma. Applying the chain rule in reverse to integration is called integration by substitution.