Problem $15.$ Find the derivative $d\frac{y}{d}x$ if

$($a$)y={\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{x}}{}}}costdt$

$($e$)y={\displaystyle \underset{\sqrt[\phantom{2}]{x}}{\overset{0}{}}}sin(t^2)dt$

$($b$)y={\displaystyle \underset{0}{\overset{x^3}{}}}{t}^{-\frac{2}{3}}dt$

$($c$)y={\displaystyle \underset{0}{\overset{tanx}{}}}se{c}^{2}tdt$

$($f$)y=n{t}_2^{x^2}sin(t^3)dt$

$($d$)y={\displaystyle \underset{0}{\overset{x}{}}}\sqrt[\phantom{2}]{1+t^2}dt$

$($g$)y={\displaystyle \underset{0}{\overset{sinx}{}}}\frac{dt}{\sqrt[\phantom{2}]{1-t^2}},|x|<mfrac><mrow><mi></mi></mrow><mrow><mn>2</mn></mrow></mfrac>$