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Question: First Principals - HSN forum

# Question: First Principals

8 replies to this topic

### #1Floorball Maniac

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Posted 01 October 2005 - 12:46 PM

Derive the following from first principals.

F(x) = e

Can someone please show me how to do it.

Thanks!

### #2Dave

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Posted 01 October 2005 - 12:57 PM

deriving from 1st principles

there is an equation which should be in your notes you just sub in values

i cant actually remember the equation and i binned my notes so not much help other than that

If i am not here i am somewhere else

### #3Steve

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Posted 01 October 2005 - 05:39 PM

The definition of the derivative of is

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### #4Floorball Maniac

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Posted 01 October 2005 - 06:33 PM

I have got that part but how do you do the simplifying in order to work it out?

### #5sparky

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Posted 01 October 2005 - 08:10 PM

Okay

x -> e^x

x+h -> e^x+h

f(x+h) - f(x) / h = e^x+h - e^x / h
= e^x . e^h - e^x / h
= e^x (e^h -1) / h
Taking out a common factor

Substitute into formula, Steve stated above
f'(x) = lim h->0 f(x+h) - f(x) / h
= lim h->0 e^x (e^h -1) / h
= e^x . 1
= e^x
Mark

### #6Floorball Maniac

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Posted 02 October 2005 - 10:33 AM

Thanks! I got most of that apart from a couple of lines.

QUOTE(sparky @ Oct 1 2005, 09:10 PM)
= lim h->0  e^x (e^h -1) / h
= e^x . 1

How did you get that above? I thought you put 0 in place of h but would that not give you 0 since you are dividing by 0?

### #7dfx

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Posted 02 October 2005 - 11:05 AM

Yeah, so as it tends to infinity....

### #8Steve

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Posted 04 October 2005 - 06:57 PM

You can't go straight from to the answer since taking h to zero would require dividing by zero.

We have to get rid of the h on the bottom line somehow...

Suppose we have:

So .

Hope that helps in some way
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### #9Floorball Maniac

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Posted 05 October 2005 - 05:13 PM

Great help, thanks!

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