Question

find dy/dx y=sqrt x raised to root x raised again to root x until infinity find dy/dx y=sqrt x raised to root x raised again to root x until infinity @Mathematics

Answer 1

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Answer 2

If y = sqrt x ^ sqrt x ^ ...
then
ln y = ln ( sqrt x ^ ... )
now ln(a^b) = b ln a. So pull out the exponent, which is also y. Hence

ln y = y ln (sqrt x) = 1/2 . y . ln x

Now differentiate both sides with respect to y

y'/y = 1/2 ( y' ln x - y / x)

Now solve for y'