Good eye -- for f(x) = x^(2x) you can not use the power rule as suggested by what follows

Power rule d (u^n)/dx = nu^(n-1)du/dx if n is a real number

however for x^(2x)

write y = x^(2x)

lny = 2xln(x)

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

y ' = x^(2x)[2ln(x) + 2] but most certainly is not 2x*x^(2x-1)