Question

what is the derivative of \[x^{x}^{x}^{x}^{x}^{x}^{x}\]

Answer 1

?

Answer 2

simple!!

Answer 3

put y=x^y

Answer 4

do logarithmic differentiation

Answer 5

but is it till infinity ?
then y=x^y would work

Answer 6

is that\[\huge x^{x^{x^{x^{...}}}}\]

Answer 7

y=x^x^x^x^x^x^x
lny=(x^x^x^x^x^x) lnx

Answer 8

Now, do differentiation

Answer 9

yes muushla

Answer 10

i assumed @Zekarias meant that

Answer 11

then y=x^y will definately do...take log on both sides.

Answer 12

then,
lny=y lnx

Answer 13

Blunder

Answer 14

@Joseph91 what blundeR?

Answer 15

@Zekarias did u get the answer?

Answer 16

It is-not an infinite series

Answer 17

IS it (1-y lnx)/x

Answer 18

yap thanks

Answer 19

LET y=x^x^x^x^x...
then
lny=ln(x^x^x^x^x...)
lny=ylnx
d(lny)/d(x) = d(y lnx)/dx

Answer 20

This will lead to the solution

Answer 21

yes thats correct mr .sauravshakya

Answer 22

But this is not suit for the questioon