I apologize for the terrible title, I'm not sure of the right way to say it.
Consider an equation which outputs in Watts $ \frac{kg \cdot m^2}{s^3} $. If you derivative out all the changes in kilograms, meters, and seconds what does the final result tell you?
Each time you take a derivative, it can come with a unit attached. Watts is already sort of a derived quantity. If I write Watts = $\frac d{dt}$Energy, we see that Watts has one more power of time in the denominator than Energy. Going the other way, we can integrate Watts $dt$ to get energy. Formally, you could take $\frac d{dx}$ Watts and get something with units $\frac {kg \cdot m}{s^3}$ but I don't have any physical sense for what it would be.