If \(f(x)=3^{2x}\), then \(f'(x) =\)

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Given an exponential function,

$$ f(x)=a^x $$ $$ f'(x)=(\ln a)a^x x' $$

For our equation,

$$ f'(x)= (\ln 3)3^{2x}\cdot 2 $$

\(2\ln3 \) can be written as \(\ln 3^2\)

$$ = \boxed{3^{2x}\ln 9} $$