Derivative of Function of Constant Multiple/Corollary

Corollary to Derivative of Function of Constant Multiple
Let $f$ be a real function which is differentiable on $\R$. Let $a, b \in \R$ be constants.

Then:
 * $\map {\dfrac \d {\d x} } {\map f {a x + b} } = a \, \map {\dfrac \d {\map \d {a x + b} } } {\map f {a x + b} }$

Proof
First it is shown that $\map {\dfrac \d {\d x} } {a x + b} = a$:

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