Derivative of Identity Function/Corollary

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Corollary to Derivative of Identity Function

$\dfrac {\mathrm d} {\mathrm d x} \left({c x}\right) = c$

where $c$ is a constant.


Proof

\(\displaystyle \frac {\mathrm d} {\mathrm d x} \left({c x}\right)\) \(=\) \(\displaystyle c \frac {\mathrm d} {\mathrm d x} x\) Derivative of Constant Multiple
\(\displaystyle \) \(=\) \(\displaystyle c \times 1\) Derivative of Identity Function
\(\displaystyle \) \(=\) \(\displaystyle c\)

$\blacksquare$


Sources