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This question already has an answer here: The $100$th derivative of $(x^2 + 1)/(x^3 - x)$ (1 answer) Closed last year .

A friend suggested me a rather tricky problem, namely find the $100^{th}$ derivative of $$ f(x)=\frac{x^2+1}{x^3-x}. $$ I have computed the zeroth derivative $$ \frac{x^2+1}{x^3-x} $$ and the first derivative $$ \frac{2x(x^3-x)-(3x^2-1)(x^2+1)}{(x^3-x)^2}=\frac{1-x^4-4x^2}{(x^3-x)^2} $$ but I don't see any obvious structure.