Write the composite function in the form $f\{g(x)\}$ with $($i$)$ identifying the inner function $u=g(x)$ and the outer function $y=f(u).$ Then, $($ii$)$ find the derivative dyr$/$dx$.$

$($a$)y=\sqrt[\phantom{2}]{43x}$

$($b$)y=sin\sqrt[\phantom{2}]{1x^3}$