Question

y=x^(x^(x^(x^(x^(x^(x....)))))) then what is xdy/dx?

Answer 1

i am getting something like y^2/(1-in x)

Answer 2

sorry, not in, thats ln

Answer 3

take y=x^y
then take log in both sides and then differenciate w.r.t x

Answer 4

y^2/(1-ylogx)

Answer 5

lny=ylnx
lny/y=lnx now differentiatie y'(1-lny)/y^2=1/x ,xy'=y^2/(1-ln y)

Answer 6

yup.. i missed y in the denominator.. :(

Answer 7

y^2/(1-y ln x)

Answer 8

err when you differentiate there wont be lnx term.

Answer 9

there will be

Answer 10

lny/y=lnx when you differentiate you get 1/x where is ln x???

Answer 11

ln y= y lnx
when u differenciate wrt x, u will get a ln x term in RHS as per the differenciation rule of form uv
d (uv)= udv+vdu

Answer 12

Oh actually its the same ylnx=lny \m/

Answer 13

well.. u will try to solve it by taking ln y=ln y ???

Answer 14

It is indeed the case that
y = x^y

Hence
\[ y' = y'.y.x^{y-1} \]
\[ \implies xy' = y'.y.x^y \]