Use logarithmic differentiation to find the derivative of the function

Question

y=(lnx)^(1/x)

Answer 1

Step 1:

The function is .

Apply logarithm on each side.

Use power rule of logarithm : .

Now apply derivative on each side with respect to .

Use product rule of derivative : .

Use logarithmic differentiation : .

                  ( Since )

Solution :

.