I want to evaluate the partial derivative of the integral stated below, with respect to $x$ and $\dot x$, respectively.
The integral is $I=\dot x \int \frac {1}{\dot {x}^2} f (x,\dot x) d\dot x$
I know about Leibnitz Rule but it is applicable only for definite integrals. Should I just interchange the differentiation and integration signs and carry out the necessary calculations?