Nth derivative of algebraic function

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The discussion focuses on finding the nth derivative of an algebraic function by utilizing specific values of x to establish relationships among coefficients A, B, and C. Participants suggest substituting values such as x=1, x=-3/2, and x=0 to generate a system of equations that can simplify the problem. This method is confirmed to be effective for deriving the nth derivative without excessive complexity.

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  • Familiarity with the concept of nth derivatives
  • Basic knowledge of solving systems of equations
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Find nth derivative of following algebraic function:

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Nice approach! I would try plugging in specific values of $x$. The $A,B,C$ relation you have found must hold for all $x$, so it should hold for, say, $x=1$ and $x=-3/2$. Then I would just pick another nice value for $x$, say, $x=0$. You get three equations in three unknowns, technically, but I don't think it'll end up being that complicated.
 

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