$($a$)$ Find $dy,$ and $($b$)$ evaluate dy for the given value of $x$ and $dx.$

$y=x\sqrt[\phantom{2}]{9-x^2},x=0,dx=0\mathrm{.}4$

$($a$)dy=1,dx$

$($Type an exact answer, using radicals as needed.$)$

$($b$)$ At the given values, dy $=$

$($Type an integer or a decimal.$)$