If $m^{\prime }\left(2\right)=7$ and $n^{\prime }\left(2\right)=-5$, find the value of ${(m+n)}^{\prime }\left(2\right)$.

Calculate the derivative of the function $g\left(x\right)=\frac{x^3}{3}+5$.

A small town's expansion is modeled by the function $S\left(t\right)=-\frac{1}{40}{t}^2+3t+15$, for $0 ≤ t ≤ 60$, where $S$ represents the area in square kilometers and $t$ is the number of years since $2000$. If the population density remains steady at $800$ people per square kilometer, what is the population growth rate in $2025$?

The graphs of $f$ and $g$ are shown. Find $H^{\prime }\left(3\right)$ if $H=f-g$.