Differentiate w.r.t. x the function (log x) log x , x 1

Question

Differentiate w.r.t. x the function (log x) log x , x > 1

Philoid · Accepted Answer

Let y =

Taking logarithm on both sides

⇒ log y = log (log x)^{log x} = log x × log (log x)

Differentiating both sides with respect to x, we get

⇒

∴