1) Let's calculate the first derivative of this function, making use of the best property:
[tex]\begin{gathered} P(t)=20-\lbrack\frac{6}{t+1}\rbrack \\ P^{\prime}(t)=\frac{d}{dt}\lbrack20\rbrack-6\cdot\frac{d}{dt}\lbrack\frac{1}{t+1}\rbrack \\ P^{\prime}(t)=0+6\cdot\frac{\frac{d}{dt}\lbrack t+1\rbrack}{(t+1)^2} \\ P^{\prime}(t)=6\cdot\frac{(1+0)}{(t+1)^2} \\ P^{\prime}(t)=\frac{6}{(t+1)^2} \end{gathered}[/tex]Note that we have differentiated separately the summands pulling out the constant factors, and then used the reciprocal rule and rewrote 6/t+1 as 6*1/t+1.
2) And that is the answer.
