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Which of the following is NOT true if $y=f(x)=\ln(e^x)^3$?

$f'(x)=\cfrac{3}{e^x}$

$y'=\cfrac{3(e^x)^2(e^x)}{(e^x)^3}$

$\cfrac{dy}{dx}= e^{-3x} \cdot (3e^{3x})$

$\cfrac{d}{dx}(f(x))=3$