Question

if y=√x^√x^√x...infinity find dy/dx​

Answer 1

Answer:

y=√x^x^x^x…………infinity.

or. y^2 =x^x^x^x………..infinity……………(1)

or. y^2 = x^y^2. Taking log both sides.

or. 2.log y = y^2.log x.

or. 2.1/y.(dy/dx) = y^2.1/x+2y.dy/dx.log x.

or. 2/y.(dy/dx)-2y.(dy/dx).log x = (y^2)/x.

or. 2.(dy/dx).(1/y- y.log x)= (y^2)/x.

or. 2.(dy/dx).(1-y^2.log x)/y =(y^2)/x.

or. dy/dx= (y^3)/2x.(1-y^2.log x).

Answer 2

Answer:

Step-by-step explanation:

Hey mate here is your answer:

→$\frac{dy}{dx} = \frac{1}{2\sqrt{x+\sqrt{x+\sqrt{x+...} } } }$,

$\huge\boxed{\text{Hope it helps you}}$