Derivative of Exponential Function/Corollary 1
Jump to navigation
Jump to search
Corollary to Derivative of Exponential Function
Let $\exp x$ be the exponential function.
Let $a \in \R$.
Then:
- $\map {\dfrac \d {\d x} } {\map \exp {a x} } = a \map \exp {a x}$
Proof
\(\ds \map {\dfrac \d {\d x} } {\map \exp {a x} }\) | \(=\) | \(\ds a \map {\dfrac \d {\map \d {a x} } } {\map \exp {a x} }\) | Derivative of Function of Constant Multiple | |||||||||||
\(\ds \) | \(=\) | \(\ds a \map \exp {a x}\) | Derivative of Exponential Function |
$\blacksquare$
Sources
- 1944: R.P. Gillespie: Integration (2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Integration of Elementary Functions: $\S 7$. Standard Integrals: $3$.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $6$: Derivatives
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $7$: Derivatives