how about; why is: Dx(e^x) = e^x : considered a seperate rule from general exponential derivatives?

Question

anonymous · Answer

U should be careful, u will be turned into an analyst before u know it....:-)

amistre64 · Answer

::: looks to see if its a full moon :::

amistre64 · Answer

$$[B^x]'=B^x\ ln(B)\ x'$$
$$[e^x]'=e^x\ ln(e)\ x'$$
right?

zarkon · Answer

yes

amistre64 · Answer

why do we need 2 rules for this one then?

myininaya · Answer

lol

zarkon · Answer

you don't

myininaya · Answer

B can equal e

amistre64 · Answer

my teacher said e was a special case ...

myininaya · Answer

amistre what are you doing to yourself?

anonymous · Answer

Consult generalized power rules....

amistre64 · Answer

im staving off going comatose from the onslaught of algbra

zarkon · Answer

only because ln(e)=1

myininaya · Answer

why does 1=0 again zarkon?

anonymous · Answer

are you supposed to prove that the derivative of 
$$e^x$$ is 
$$e^x$$?

zarkon · Answer

lol...don't thin i want to go there ;)

myininaya · Answer

lol

anonymous · Answer

i think this depends largely on your definition of e

myininaya · Answer

i thought amistre has taken calculus

anonymous · Answer

Rule 1 - I f something doesn't work properly, redefine it.

Rule 2 - I f it still doesn't work, generalize it.

amistre64 · Answer

i taught myself calculus; going thru the courses now tho

myininaya · Answer

wow amistre you are so smart

anonymous · Answer

one definition is that it is the number that works.  you can see that the derivative of 
$$2^x=2^x\lim_{h\rightarrow 0}\frac{2^h-1}{h}$$

myininaya · Answer

theres no way i could have done that

amistre64 · Answer

... i wasnt smart enough to know 0^0 was bad lol

anonymous · Answer

and the derivative of 
$$3^x=3^x\lim_{h\rightarrow 0}\frac{3^h-1}{h}$$

amistre64 · Answer

why is the derivative of e^x a seperate rule from B^x, is my question in general

anonymous · Answer

e^x came from logs....

myininaya · Answer

there is no reason they should be separate

anonymous · Answer

one limit is less than 1, one is greater, and you can define e to be the number such that 
$$\lim_{h\rightarrow 0}\frac{e^h-1}{h}=1$$

anonymous · Answer

that gives it to you.

myininaya · Answer

think they talk about the rule d(e^x)=e^x first  because it is easiest

anonymous · Answer

actually i think e came from exponential growth, not from logs but i might be mistaken.  pretty sure though.  euler looking at continuous growth

myininaya · Answer

i want a potato

anonymous · Answer

Logs, very interesting history, u would like it....

anonymous · Answer

starting with napier?

anonymous · Answer

Yup...

anonymous · Answer

potato mmmm
 too many carbs for me

anonymous · Answer

Working it in as an inverse came later...

amistre64 · Answer

i tend to start earlier; with thag and goor :)

anonymous · Answer

used as calculator as i remember but not really logs as we think of them

amistre64 · Answer

caveman maths

anonymous · Answer

|dw:1314234822359:dw|

anonymous · Answer

e was there, just didn't calculate it as e.

anonymous · Answer

napier?  i need a book

anonymous · Answer

@estudier did you prove 1/4 is in the cantor set?

amistre64 · Answer

napier and...bernolli ?

anonymous · Answer

must have been some bernoulli.  they did everything.

anonymous · Answer

http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3209&bodyId=3453

anonymous · Answer

1/4 is in the ternary cantor set (obviously)