# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2021-05-15 02:26:32

mathland
Member
Registered: 2021-03-25
Posts: 444

### Derivative of e^(x) = e^(x)

I know that d/dx [e^(x)] = e^(x).

My question:

Why is this the case?

Why is e^(x) its own derivative?

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## #2 2021-05-15 02:55:57

zetafunc
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Registered: 2014-05-21
Posts: 2,435
Website

### Re: Derivative of e^(x) = e^(x)

It might help to consider what we actually mean by e^x.

What is the definition of e^x?

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## #3 2021-05-15 04:41:40

mathland
Member
Registered: 2021-03-25
Posts: 444

### Re: Derivative of e^(x) = e^(x)

zetafunc wrote:

It might help to consider what we actually mean by e^x.

What is the definition of e^x?

1. The hint does not help.

2. Can you explain in MATH FOR DUMMIES style of language?

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## #4 2021-05-15 05:23:55

Bob
Registered: 2010-06-20
Posts: 10,514

### Re: Derivative of e^(x) = e^(x)

hi mathland

Somehow I knew in advance that you would want to know about this so I searched back through all my posts and found this:

http://www.mathisfunforum.com/viewtopic.php?id=25550

My last post in the thread was an offer to finish the lessons but only if the guy was interested.  I got no response then, but the offer still stands.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #5 2021-05-15 06:33:03

mathland
Member
Registered: 2021-03-25
Posts: 444

### Re: Derivative of e^(x) = e^(x)

Bob wrote:

hi mathland

Somehow I knew in advance that you would want to know about this so I searched back through all my posts and found this:

http://www.mathisfunforum.com/viewtopic.php?id=25550

My last post in the thread was an offer to finish the lessons but only if the guy was interested.  I got no response then, but the offer still stands.

Bob

Please, finish the lesson. I am interested. This is a lot to digest but not if I divide the reading into 2 or 3 days.

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## #6 2021-05-15 06:35:40

Bob
Registered: 2010-06-20
Posts: 10,514

### Re: Derivative of e^(x) = e^(x)

B

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #7 2021-05-15 07:16:08

mathland
Member
Registered: 2021-03-25
Posts: 444

Bob wrote: