I was considering the derivation of the expression for power from work.
If $W=\int_{\underline r_1}^{\underline r_2} \underline F(t) . d\underline r$
And here I think I can put either $F(t)$ or $F(\underline r)$ because technically F can be written as a function of either.
But here is my problem: I don't know if differentiating under the integral sign is permitted for dependent variables.
i.e. if $P=\frac{dW}{dt} = \frac{d}{dt}\int_{\underline r_1}^{\underline r_2} \underline F(t) . d\underline r$
can I do any differentiation under the integral sign here?