​ If y = x^{x^x.......∞} then dy/dx = ? A. y/x(1-log x) B. y^2/x(1-log x) C. y/x(1-y log x) D. none of these ​

Question

If y = \(x^{x^{x.....\infty}}\) then dy/dx = ?

A. y/x(1-log x)

B. y²/x(1-log x)

C. y/x(1-y log x)

D. none of these

Answer 1

Answer is: B. y²/x(1-log x)

Given:

⇒ y = \(x^{x^{x.....\infty}}\)

We can write it as

⇒ y = x^y

Taking log of both sides we get

log y = y log x

Differentiating