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Proof: The derivative of 𝑒ˣ is 𝑒ˣ

AP.CALC:
FUN‑3 (EU)
,
FUN‑3.A (LO)
,
FUN‑3.A.4 (EK)
e, start superscript, x, end superscript is the only function that is the derivative of itself!
start fraction, d, divided by, d, x, end fraction, open bracket, e, start superscript, x, end superscript, close bracket, equals, e, start superscript, x, end superscript
(Well, actually, f, left parenthesis, x, right parenthesis, equals, 0 is also the derivative of itself, but it's not a very interesting function...)
The AP Calculus course doesn't require knowing the proof of this fact, but we believe that as long as a proof is accessible, there's always something to learn from it. In general, it's always good to require some kind of proof or justification for the theorems you learn.
Khan Academy video wrapper
Proof: The derivative of 𝑒ˣ is 𝑒ˣSee video transcript

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