Rate of Change

[sammiyahc0]

1.
The power delivered by a battery to an apparatus of resistance R (in ohms) is P = 2.35R /(R + 0.5)^2
watts.Find the rate of change of power with respect to resistance for R = 9.(Round your answer to four decimal places

2. quotient rule



3. 2.35(9+.05)^2-2(r+.5)/(r+0.5)^4

 

[haruspex]

You've not applied the quotient rule correctly. You dropped a factor in the second term, and a 2.35 has been reduced to 2. it would help if you included all appropriate parentheses. Why have you substituted r = 9 in some places but not in others?

 

[Ibix]

What you have written is (I think - you appear to have substituted R=9 in some places but not others):$$2.35(R+0.5)^2-\frac{2(R+0.5)}{(R+0.5)^4}$$which I don't think is right. Even assuming that you meant $$\frac{2.35(R+0.5)^2-2(R+0.5)}{(R+0.5)^4}$$I still don't think this is right. I was taught that the quotient rule as$$d\frac{u}{v}=\frac{vdu-udv}{v^2}$$Perhaps you could show us what you think $u, v, du, dv$ are?