For the function $P(t)=\frac{2500t5000}{t200}($population of a transplanted insect$),$ determine which of the following is the correct derivative $P^{\text{'}}(t).$

$P^{\text{'}}(t)=2500$

$P^{\text{'}}(t)=\frac{495000}{(t200{)}^2}$

I

$P^{\text{'}}(t)=\frac{5000t505000}{(t200{)}^2}$

$P^{\text{'}}(t)=\frac{505000}{(t200{)}^2}$

$P^{\text{'}}(t)=\frac{2500}{t200}$