Derivative of Identity Function/Corollary

Corollary to Derivative of Identity Function

$\map {\dfrac {\d} {\d x} } {c x} = c$

where $c$ is a constant.


Proof

\(\ds \map {\frac \d {\d x} } {c x}\) \(=\) \(\ds c \frac \d {\d x} x\) Derivative of Constant Multiple
\(\ds \) \(=\) \(\ds c \times 1\) Derivative of Identity Function
\(\ds \) \(=\) \(\ds c\)

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 13$: General Rules of Differentiation: $13.3$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $1$: Derivatives
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $1$: Derivatives
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