Question

Trying to find derivative of y = x^(lnx), show step-by-step solution

Answer 1

`y=x^(ln(x)) \\ ln(y)=\ln{x^(ln(x))} \\ ln(y)=ln(x)ln(x) \\ (1)/(y) dy= ((1)/(x) ln(x)+ (1)/(x) ln(x))dx \\ \\(1)/(y) y'= (2)/(x) ln(x) \\ \\y'=y(2)/(x) ln(x) \\ \\y'=x^(ln(x))(2)/(x) ln(x) \\ \\y'= (x^(ln(x))2ln(x))/(x) \\ \\y'=2x^(ln(x)-1)ln(x)`