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Kainui
 one year ago
Let's try this! @ikram002p
\[\frac{d}{dx}(a\uparrow^x b)\]
Kainui
 one year ago
Let's try this! @ikram002p \[\frac{d}{dx}(a\uparrow^x b)\]

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Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1Can i try as well?

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1Oki lol let me get paper

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4This might be an impossible question lol.

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1lol hmm nothing is impossible ;)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3i'll write what im thinking of and then lets see :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Woah let me take a stab at this!

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1Can i give you a question @Kainui :)

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ d }{ dx } (2^{x)}\] How do you find ^

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1You lost @Kainui ? tehee :)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3@Kainui lets try on small stuff like dw:1433362211420:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433362587173:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3thats only special case yes my writing

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3eh . i wish if there is a short cut

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.1lol neat hand writing :)

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3i might end up saying zero since this arrow notation end up defining a finite number hmmm but if we wanna deal with it as exponent we neat ani_arrow notation , right @Kainui ? is there something like this ??

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4Sorry I got distracted right as I posted this orry! Good idea on using the 2 case, that's awesome!

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4One way I was thinking of is seeing if we could weasel our way into a continuous definition of the arrow notation with the definition of derivative: \[\large \lim_{h \to 0}\frac{a \uparrow^{x+h} b  a \uparrow^x b }{h}\]

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4For anyone who doesn't know the arrow notation, which to be honest I barely do either. \[ a \uparrow b = a^b \\ a \uparrow \uparrow b = a^{a^{a^\cdots}} \text{tower b high}\] So the recursive definition is found here, but I'llt ype it out too: \[a \uparrow ^n b = a \uparrow ^{n1}[a \uparrow^n(b1)]\] and \[a \uparrow^n 1 = a\] http://mathworld.wolfram.com/PowerTower.html So for example: \[4 \uparrow^2 3 = 4 \uparrow (4 \uparrow^2 2)=4 \uparrow (4 \uparrow (4 \uparrow^2 1)) = 4 \uparrow (4 \uparrow (4 )) = 4^{4^4}\]

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0I don't know, but I think we may need to look at how \(\uparrow^x\) is defined for any real value of x?

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4Yeah it relies on making this definition which is discrete into something continuous which might not really even be possible.

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4Here I should have posted this to begin with for those who aren't into this yet! http://www.numberphile.com/videos/grahamsnumber.html

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4Another example, here are our rules just for reference: \[a \uparrow ^n b = a \uparrow ^{n1}[a \uparrow^n(b1)]\] \[a \uparrow^n 1 = a\] Ok so the example: \[4 \uparrow^3 3 \] Just plug and chug that recursion relation:\[ 4 \uparrow^2 (4 \uparrow^3 2) \]Now just looking at that part \((4 \uparrow^3 2)\) I expand that further:\[ 4 \uparrow^2 (4 \uparrow^2(4 \uparrow^3 1)) \] now using the fact that \((4 \uparrow^n 1) = 4 \) also listed above as the other rule we have: \[ 4 \uparrow^2 (4 \uparrow^24) \] Which we then expand further

Kainui
 one year ago
Best ResponseYou've already chosen the best response.4The next step we start expanding: \[ 4 \uparrow^2 (4 \uparrow 4 \uparrow 4 \uparrow 4) = 4 \uparrow^2 4^{4^{4^4}}\] And past this we really can't do anything in terms of writing it cause this is a tower of 4s that is \(4^{4^{4^4}}\) high. lol

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Here's another problem for you to consider into: Evaluate \(\dfrac{\mathrm d^{1/2}}{\mathrm dx^{1/2}}~~\large x\) :)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0http://openstudy.com/study#/updates/556f9e4ce4b050a18e84d177

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.3a way not impossible
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