What will be the derivative $2 (\ln (x))^{x/2}$? I'm not sure, that my steps are valid, so $ln(f(x))=ln \cdot (2 \cdot ln(x))^{x/2}=x^{2} \cdot ln \cdot(ln(x))$ so I get $\frac{1}{f(x)} \cdot f'(x)$ and I have to multiply both sides with $f(x)$, am I right?

HINT
Let consider
$$2 (\ln (x))^{x/2}=2e^{(x/2)\ln x}$$
then use
$$(e^{f(x)})'=e^{f(x)}f'(x)$$
