Question

find derivative of y = x^(lnx), Show step-by-step solution

Answer 1

x^ln(x)
=x^ln(x) * ln(x)*ln(x)
=(ln^2(x))*x^ln(x)
=2ln(x)*(ln(x)*x^ln(x)) 
=2x^ln(x)-1 * ln(x) 

Answer 2

y = x^(ln x )        / ln   ( we will logarithm both sides of the equation )
$ln y = ln x^{lnx} \\ ln y = ln x * ln x \\ ln y = ln ^{2} x \\ \frac{1}{y}y`= 2 ln x * \frac{1}{x} \\ y`= \frac{2lnx}{x}*y \\ y`= \frac{2lnx*x ^{lnx} }{x}$