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 Apr 21 accepted Numerical partial derivative of an inverse function Apr 20 asked Numerical partial derivative of an inverse function Apr 18 accepted Undefined derivative of a third degree polynomial inverse? Apr 18 revised Undefined derivative of a third degree polynomial inverse? edited title Apr 18 asked Undefined derivative of a third degree polynomial inverse? Nov 20 awarded Notable Question Aug 30 awarded Popular Question Aug 16 comment Convex Quadrilateral Test This looks like an efficient solution. I have finally used Cramer's Rule to check whether intersection of diagonals lays inside the quadrilateral. Mar 7 revised Derivative of inverse function where inverse is known only numerically. deleted 18 characters in body Mar 7 answered Derivative of inverse function where inverse is known only numerically. Mar 7 revised Derivative of inverse function where inverse is known only numerically. edited title Mar 7 comment Derivative of inverse function where inverse is known only numerically. I don't see how it's trivial. The forward derivative is already a third degree polynomial in $x$. The inverse can be computed only numerically so it seems I need a special numerical approximation routine for $f^{-1}(y,a)$ as $y$ depends on $a$ and we don't have the information on how it depends on it... Mar 7 revised Derivative of inverse function where inverse is known only numerically. added 63 characters in body Mar 7 comment Derivative of inverse function where inverse is known only numerically. But I computed the inverse without problem numerically. I only need to compute it more precisely using some formula. Please note that I also care about partial derivative only (w.r.t. a), not in both variables (the x can be considered fixed). Such function can be plotted and I can see it has inverse (graphically), but I need the formula... Mar 7 comment Derivative of inverse function where inverse is known only numerically. One problem is that it is impossible to compute $J^{-1}$ in this case because it is a non-square matrix ($1\times 2$). Mar 7 comment Derivative of inverse function where inverse is known only numerically. I found it, thanks. Mar 7 comment Derivative of inverse function where inverse is known only numerically. I was looking for that without success (using keyword "multivariable inverse function theorem"). I found something called "implicit function theorem" but I am not sure if this is it nor how to apply it. Mar 7 asked Derivative of inverse function where inverse is known only numerically. Feb 25 revised Inverse function theorem for partial derivatives of a vector function added 31 characters in body Feb 25 answered Inverse function theorem for partial derivatives of a vector function