I have a line integral over a contour which has N parameters in a vector x of length N, i.e.
$ E = \oint_C f(x,y) ds $
The contour C is parametrized using parameters $ x_{i} $, entries of the vector $ x $. I want to find the derivative of this line integral wrt. $ x_{i} $ i.e. find $ \frac{\partial E}{\partial x_{i}} $
Is there a neat way to do this?