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Questions about the determinant of square matrices or linear endomorphisms. Also for closely related topics such as minors or regularized determinants.
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General formulas for derivative of $f_n(x)=\dfrac{ax^n+bx^{n-1}+cx^{n-2}+\cdots}{a'x^n+b'x^{...
You can easily extend this, but for $n\geq 3$ you will end up with more than one term per monomial:
For two functions $f$, $g$ rewrite the quotient rule using a determinant
$$\frac{d}{dx} \frac{f}{g} …