Question

Calculate the derivative of P(t) = 20 - [(6/(t+1)]

Answer 1

`P^(\prime)(t)=(6)/((t+1)^2)`

1) Let's calculate the first derivative of this function, making use of the best property:

`\begin{gathered} P(t)=20-\lbrack(6)/(t+1)\rbrack \\ P^(\prime)(t)=(d)/(dt)\lbrack20\rbrack-6\cdot(d)/(dt)\lbrack(1)/(t+1)\rbrack \\ P^(\prime)(t)=0+6\cdot((d)/(dt)\lbrack t+1\rbrack)/((t+1)^2) \\ P^(\prime)(t)=6\cdot((1+0))/((t+1)^2) \\ P^(\prime)(t)=(6)/((t+1)^2) \end{gathered}`

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.