Find the derivative of the function V(P)= k/P

[ver_mathstats]

Homework Statement

We are given the function V(P) =k/P. When 𝑉(𝑃) is measured in liters (L) and 𝑃 is measured in atmospheres (atm), the units of 𝑘, a constant based on the identity of the gas, are litres per atmosphere (L/atm). If 𝑘=8.60, what is the instantaneous rate of change of the chamber’s volume with respect to pressure, V'(P) or 𝑑𝑉/𝑑𝑃, when the gas exerts 1.30 atm of pressure on the chamber’s surface? Round your answer to the nearest tenth of a litre per atmosphere.

Find V'(1.30).

Relevant Equations

V(P) =k/P, V'(P)

I tried to find the derivative of the function V(P)= k/P which I found to be:

V'(P) = kP^-1 V'(P) = (1)(-1)(P)^-1-1 = -1/(P²)

And then I substituted in 1.30 into the derivative to obtain -0.5917 L/atm. And I am kind of confused how to actually find the derivative of this. I thought I was on the right track but I got it wrong, and I don't really know where I would use the k=8.60.

 

[fresh_42]

You have lost your constant factor $k$. For $f(x)=k\cdot g(x)$ we have $f'(x)=k\cdot g'(x)$. You substituted it by $k=1$.

 

[ver_mathstats]

You have lost your constant factor $k$. For $f(x)=k\cdot g(x)$ we have $f'(x)=k\cdot g'(x)$. You substituted it by $k=1$.

Okay, thank you. I got -5.1.