What is the rate of change of power?

[DespicableMe]

Homework Statement

POwer P in watts, produced by an engine is P(R) = 130R / [(R+0.8)² ] where R is resistance. What is the rate of change of power when R = 5?

Homework Equations

The Attempt at a Solution

I do not understand how the rate of change for this is

130/ ( (R+0.8)²) - 2(130R) / ((R+0.8)³⁾

I have tried plugging in R=5 into what I just typed above and I got the right answer. I just don't understand how they got to that equation.

One site wrote that the ROC of current with respect to resistance is 125/R², for example, if current was 125/R

Can someone please clarify?

 

[Dick]

Well, what you typed there is the derivative of P(R) with respect to R. I think that's what they are asking for. What are you confused about?

 

[DespicableMe]

Well, what you typed there is the derivative of P(R) with respect to R. I think that's what they are asking for. What are you confused about?

They simplified the form of the quotient rule, so I wasn't sure why the whole thing was over the denominator to the power of 3 instead of the power of 4.

When I did the quotient rule again, I understood where I went wrong and how they simplified it, so I have the answer now. Thanks.