Derivative of f(x)=x^x^2 ?

Question

f(x)=x^{x^2}

Answer 1

 y  = x^{x^2}

ln(y) = ln(x^{x^2}) = x² ln(x)

 

taking derivative of both sides with respect to x we have,

y^'/y = 2x ln(x)+x

y' = (2x ln(x)+x ) x^{x^2}