If $f(x)=(x-1{)}^{2}sinx,$ then $f^{\text{'}}(0)=$

$($a$)1$

$($b$)2$

$($c$)-1$

$($d$)0$

$\frac{d}{dx}(co{s}^2(x^3))=$

$($a$)-si{n}^2(x^3)$

$($b$)-6x^{2}sin(x^3)cos(x^3)$

$($c$)6x^{2}sin(x^3)cos(x^3)$

$($d$)6x^{2}cos(x^3)$

If $y=(\frac{x}{x+1}{)}^5,$ then $\frac{dy}{dx}=$

$($a$)\frac{5x^4}{(x+1{)}^4}$

$($b$)5(1+x{)}^4$

$($c$)\frac{5x^4(2x+1)}{(x+1{)}^6}$

$($d$)\frac{5x^4}{(x+1{)}^6}$

The table below gives selected values of $f,f^{\text{'}},g,$ and $g^{\text{'}}.$

$\backslash$table$[[x,f(x),f^{\text{'}}(x),g(x),g^{\text{'}}(x)$

Please :$\text{'})$