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 \\ (1)/(y)y`= 2 ln x * (1)/(x) \\ y`= (2lnx)/(x)*y \\ y`= (2lnx*x ^(lnx) )/(x)`