- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- Here_to_Help15

Can i try as well?

- Kainui

Yeah anyone can lol

- Here_to_Help15

Oki lol let me get paper

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- Kainui

This might be an impossible question lol.

- Here_to_Help15

lol hmm nothing is impossible ;)

- ikram002p

i'll write what im thinking of and then lets see :)

- anonymous

Woah let me take a stab at this!

- Here_to_Help15

Can i give you a question @Kainui :)

- Here_to_Help15

\[\frac{ d }{ dx } (2^{x)}\]
How do you find ^

- Here_to_Help15

You lost @Kainui ? tehee :)

- ikram002p

@Kainui
lets try on small stuff like
|dw:1433362211420:dw|

- ganeshie8

* for tomoro

- Here_to_Help15

?

- ikram002p

|dw:1433362587173:dw|

- Here_to_Help15

Is that

- Here_to_Help15

Your writing

- ikram002p

thats only special case
yes my writing

- ikram002p

eh -.- i wish if there is a short cut

- Here_to_Help15

lol neat hand writing :)

- ikram002p

ty :)

- ikram002p

i 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

Sorry I got distracted right as I posted this orry!
Good idea on using the 2 case, that's awesome!

- Kainui

One 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

For 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:
\[a \uparrow ^n b = a \uparrow ^{n-1}[a \uparrow^n(b-1)]\]
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

I don't know, but I think we may need to look at how \(\uparrow^x\) is defined for any real value of x?

- Kainui

Yeah it relies on making this definition which is discrete into something continuous which might not really even be possible.

- Kainui

Here I should have posted this to begin with for those who aren't into this yet!
http://www.numberphile.com/videos/grahamsnumber.html

- Kainui

Another example, here are our rules just for reference:
\[a \uparrow ^n b = a \uparrow ^{n-1}[a \uparrow^n(b-1)]\]
\[a \uparrow^n 1 = a\]
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

The 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

Here's another problem for you to consider into:
Evaluate \(\dfrac{\mathrm d^{1/2}}{\mathrm dx^{1/2}}~~\large x\)
:)

- ikram002p

a way not impossible

Looking for something else?

Not the answer you are looking for? Search for more explanations.