given the following function as an toy example:
$f(\alpha,\beta) = \frac{c_1 \cdot sin(\alpha - asin(c_2))}{sin(\alpha-\beta-c_3)}$
where $c_1,c_2,c_3$ are some constants.
Knowing the points of discontinuity, I would get in a next step the derivative of this example by performing a partial derivative according to $\alpha$ and $\beta$.
For this purpose I'd like to exclude the points of discontinuity from the derivation. Is this possible to partially derivate $f(\alpha,\beta)$ only for specific intervals of $\alpha,\beta$? My primary purpose is not to get a explicit solution for the toy function but rather to see if it is possible - and if yes - how one can perform partial derivatives on such a discontinuous trigonometric function.
Thank you in advance for any directing hints. Dan