Power of an electrical circuit is equal to current squared times resistance. My expression for current is: E/(R + r), where E is emf of battery. So, my expression for Power, P, is: P=((E^2)R)/(R + r)^2 I would like to differentiate P with respect to R, to find where the slope is zero, ie., the maximum power. I am having some trouble though. I used the quotient rule and got: ((R + r)E^2 - 2RE^2)/(R + r)^3 Is this correct? I need to know where this is zero, but I am a bit unsure about where to go from here.