Let $g(x)={\displaystyle \underset{0}{\overset{x}{}}}sin({}^2)d.$

$($a$)(2$ points$)$ On the interval $0,\sqrt[\phantom{2}]{2},$ sketch the function $y=sin({}^2)$

$($b$)(2$ points$)$ When does $g(x)$ reach its minamum relue? Describe why is terms of area and integrals.

$($c$)(4$ points$)$ What is $g^{\text{'}}(x)?g^{\text{'}}(\sqrt[\phantom{2}]{2})?$

$($d$)(2$ points$)$ What is $\frac{d}{dx}(g(x^4))?$

$($e$)(2$ points$)$ What is $\frac{d}{dx}({\displaystyle \underset{0}{\overset{x^4}{}}}sin({}^2)d)?$