Cálculo de funciones derivadas

Derívese la función $y=(2^{x})^x$

$y=(2^{x})^x=2^{x\cdot x}=2^{x^2}=\left(e^{\ln(2)}\right)^{x^2}=e^{x^2\cdot \ln(2)} \therefore$
  $\therefore y'=e^{x^2\cdot \ln(2)} \cdot (x^2\cdot \ln(2))'=2\,\ln(2)\cdot x\cdot e^{x^2\cdot \ln(2)} = 2\,\ln(2)\cdot x\cdot 2^{x^2} = 2\,\ln(2)\cdot x\cdot (2^{x})^x =$
    $= \ln(2^2)\cdot x\cdot (2^{x})^x = \ln(4)\cdot x\cdot (2^{x})^x$
$\diamond$