Find the derivative of
I recommend Scott's method.
Change the function to:
$\displaystyle y = e^{4^x\ln{x}}$
Then you differentiate:
$\displaystyle y' = e^{4^x\ln{x}}\frac{d}{dx}[4^x\ln{x}]$
All you use now is the product rule.
$\displaystyle y' = e^{4^x\ln{x}}\left(4^x\log{4}\ln{x} + \frac{4^x}{x}\right)$
We remember that: $\displaystyle e^{4^x\ln{x}} = x^{4^x}$
$\displaystyle y' = 4^xx^{4^x}\left(\ln{x}\log{4} + \frac{1}{x}\right)$