If $f$ is a vector$-$valued function defined by $f(t)=(e^{-t},cost),$ then $f^{\text{'}\text{'}}(t)=$

$($A$)-e^{-t}+sint$

$($B$)e^t-cost$

$($C$)(-e^{-t},-sint)$

$($D$)(e^{-t},cost)$

$($E$)(e^{-t},-cost)$

A particle moves in the $xy-$plane so that its position at time $t>0$ is given by $x(t)=2lnt$ and $y(t)=\frac{4}{t+1}.$ What is the speed of the particle when $t=1?$

$($A$)1$

$($B$)\sqrt[\phantom{2}]{2}$

$($C$)2$

$($D$)\sqrt[\phantom{2}]{5}$