Answer to Question #1912 in Calculus for Bujju

Question

Use logarithmic differentiation to find the derivative of the function.
y = x^ln(x)

Answer 1

x^lnx = e ^{ln(x^(ln(x))} = e ^{lnx lnx}

y' = ( e ^{lnx lnx} )' = e ^{lnx lnx} *2 lnx * 1/x =2 x^lnx-1 * lnx