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