Let $r(x)=f(g(h(x))),$ where $h(1)=5,g(5)=3,h(1)=3,g(5)=4,$ and $f^{\text{'}}(3)=8.$ Find $r^{\text{'}}(1).$

$[-/1$ Points$]$

$r(1)=$

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$[-/2$ Points$]$

SEssCalcE

If the equation of motion of a particle is given by $s=$Acos$(t),$ the particle is said to undergo harmanic motion.

$($a$)$ Find the velocity of the particle at time $t.$

$s^{\text{'}}(t)=$

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$($b$)$ When is the velocity $0?($Use $n$ as the arbitrary integer.$)$

$t=$

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$[-/1$ Points$]$

SEssd

If $F(x)=f(5f(8f(x))),$ where $f(0)=0$ and $f^{\text{'}}(0)=1,$ find $F^{\text{'}}(0).$

$F^{\text{'}}(0)=$