Question

how to solve y=x^(lnx) using log diff.?

Answer 1

\[\ln(y)=\ln(x) \cdot \ln (x)\]

Answer 2

then differentiate both sides:
\[{d \over dx}\left[ \ln y \right]={d \over dx}\left[ \left( \ln x \right)^2 \right]\]

Answer 3

\[\frac 1y \cdot {dy \over d x}=2\ln x \cdot \frac 1x\]

\[\implies {dy \over d x}=2\ln x \cdot \frac yx\]... finally replace y with x^(lnx)