Let $y(x)=(2x^2+3x{)}^2$ and $z(x)=\frac{x}{\sqrt[\phantom{2}]{x^2-1}}.$

$($a$)$ Calculate the first derivative $y^{\text{'}}(x).$

$($b$)$ Calculate the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}y(x)dx.$

$($c$)$ Calculate the first derivative $z^{\text{'}}(x).$

$($d$)$ Calculate the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}z(x)dx.$